bluuebunny/crossref_metadata_2025 huggingface dataset:
The emptiness problem for intersection types
Authors: Urzyczyn Paweł
Published: May 2006

We study the intersection type assignment system as defined by Barendregt, Coppo and Dezani. For the four essential variants of the system (with and without a universal type and with and without subtyping) we show that the emptiness (inhabitation) problem is recursively unsolvable. That is, there is no effective algorithm to decide if there is a closed term of a given type. It follows that provability in the logic of “strong conjunction” of Mints and Lopez-Escobar is also undecidable.
Quasi-o-minimal structures
Authors: Belegradek Oleg , Peterzil Ya'acov , Wagner Frank
Published: May 2006

A structure (M, <, …) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1.
On the equational theory of representable polyadic equality algebras
Authors: Németi István , Sági Gábor
Published: May 2006

Among others we will prove that the equational theory of ω dimensional representable polyadic equality algebras (RPEAω's) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable (and hence the equational theory of this class is finite schema-axiomatizable. as well). We will also show that the complexity of the equational theory of RPEAω is also extremely high in the recursion theoretic sense. Finally, comparing the present negative results with the positive results of Ildikó Sain and Viktor Gyuris [12], the following methodological conclusions will be drawn: The negative properties of polyadic (equality) algebras can be removed by switching from what we call the “polyadic algebraic paradigm” to the “cylindric algebraic paradigm”.
A 1-generic degree with a strong minimal cover
Authors: Kumabe Masahiro
Published: May 2006

We consider a set generic over the arithmetic sets. A subset A of the natural numbers is called n-generic if it is Cohen-generic for n-quantifier arithmetic. This is equivalent to saying that for every -set of strings S, there is a string σ ⊂ A such that σ ∈ S or no extension of σ is in S. By degree we mean Turing degree (of unsolvability). We call a degree n-generic if it has an n-generic representative. For a degree a, let D(≤ a) denote the set of degrees which are recursive in a.

We say a is a strong minimal cover of g if every degree strictly below a is less than or equal to g. In this paper we show that there are a degree a and a 1-generic degree g < a such that a is a strong minimal cover of g. This easily implies that there is a 1-generic degree without the cupping property. Jockusch [7] showed that every 2-generic degree has the cupping property. Slaman and Steel [17] and independently Cooper [3] showed that there are recursively enumerable degrees a and b < a such that no degree c < a joins b above a. Take a 1-generic degree g below b. Then g does not have the cupping property.
Higher gap morasses, Ia: Gap-two morasses and condensation
Authors: Morgan Charles
Published: May 2006

This paper concerns the theory of morasses. In the early 1970s Jensen defined (k, α)-morasses for uncountable regular cardinals k and ordinals α < k. In the early 1980s Velleman defined (k, 1)-simplified morasses for all regular cardinals k. He showed that there is a (k, 1)-simplified morass if and only if there is (k, 1)-morass. More recently he defined (k, 2)-simplified morasses and Jensen was able to show that if there is a (k, 2)-morass then there is a (k, 2)-simplified morass.

In this paper we prove the converse of Jensen's result, i.e., that if there is a (k, 2)-simplified morass then there is a (k, 2)-morass.
On the existence of strong chains in ℘(ω1)/Fin
Authors: Koszmider Piotr
Published: May 2006

(Xα: α < ω2) ⊂ ℘(ω1) is a strong chain in ℘(ω1)/Fin if and only if Xβ – Xα is finite and Xα – Xβ is uncountable for each β < α < ω1. We show that it is consistent that a strong chain in ℘(ω1) exists. On the other hand we show that it is consistent that there is a strongly almost-disjoint family in ℘(ω1) but no strong chain exists: is used to construct a c.c.c forcing that adds a strong chain and Chang's Conjecture to prove that there is no strong chain.
The independence of the Prime Ideal Theorem from the Order-Extension Principle
Authors: Felgner U. , Truss J. K.
Published: May 2006

It is shown that the boolean prime ideal theorem BPIT: every boolean algebra has a prime ideal, does not follow from the order-extension principle OE: every partial ordering can be extended to a linear ordering. The proof uses a Fraenkel–Mostowski model, where the family of atoms is indexed by a countable universal-homogeneous boolean algebra whose boolean partial ordering has a ‘generic’ extension to a linear ordering. To illustrate the technique for proving that the order-extension principle holds in the model we also study Mostowski's ordered model, and give a direct verification of OE there. The key technical point needed to verify OE in each case is the existence of a support structure.
Upper bounds for standardizations and an application
Authors: Xi Hongwei
Published: May 2006

We present a new proof for the standardization theorem in λ-calculus, which is largely built upon a structural induction on λ-terms. We then extract some bounds for the number of β-reduction steps in the standard β-reduction sequence obtained from transforming a given β-reduction sequence, sharpening the standardization theorem. As an application, we establish a super exponential bound for the lengths of β-reduction sequences from any given simply typed λ-terms.
Uniform inseparability in explicit mathematics
Authors: Cantini Andrea , Minari Pierluigi
Published: May 2006

We deal with ontological problems concerning basic systems of explicit mathematics, as formalized in Jäger's language of types and names. We prove a generalized inseparability lemma, which implies a form of Rice's theorem for types and a refutation of the strong power type axiom POW+. Next, we show that POW+ can already be refuted on the basis of a weak uniform comprehension without complementation, and we present suitable optimal refinements of the remaining results within the weaker theory.
On the No-Counterexample Interpretation
Authors: Kohlenbach Ulrich
Published: May 2006

In [15], [16] G. Kreisel introduced the no-counterexample interpretation (n.c.i.) of Peano arithmetic. In particular he proved, using a complicated ε-substitution method (due to W. Ackermann), that for every theoremA(Aprenex) of first-order Peano arithmeticPAone can find ordinal recursive functionalsof order type < ε0which realize the Herbrand normal formAHofA.

Subsequently more perspicuous proofs of this fact via functional interpretation (combined with normalization) and cut-elimination were found. These proofs however do not carry out the no-counterexample interpretation as alocalproof interpretation and don't respect the modus ponens on the level of the nocounterexample interpretation of formulasAandA → B. Closely related to this phenomenon is the fact that both proofs do not establish the condition (δ) and—at least not constructively—(γ) which are part of the definition of an ‘interpretation of a formal system’ as formulated in [15].
The Complexity of the Collection of Countable Linear Orders of the form I + I
Authors: Beleznay Ferenc
Published: May 2006

First we prove that the set of countable linear orders of the form I + I form a complete analytic set. As a consequence of this we improve a result of Humke and Laczkovich, who showed in [HL] that the set of functions of the form f º f form a true analytic set in C[0,1]. We show that these functions form a complete analytic set, solving a problem mentioned on p. 215 of [Kl] and on p. 4 of [B]
DOP and FCP in generic structures
Authors: Baldwin John T. , Shelah Saharon
Published: May 2006

We work throughout in a finite relational language L. This paper is built on [2] and [3]. We repeat some of the basic notions and results from these papers for the convenience of the reader but familiarity with the setup in the first few sections of [3] is needed to read this paper. Spencer and Shelah [6] constructed for each irrational α between 0 and 1 the theory Tα as the almost sure theory of random graphs with edge probability n−α. In [2] we proved that this was the same theory as the theory Tα built by constructing a generic model in [3]. In this paper we explore some of the more subtle model theoretic properties of this theory. We show that Tα has the dimensional order property and does not have the finite cover property.

We work in the framework of [3] so probability theory is not needed in this paper. This choice allows us to consider a wider class of theories than just the Tα. The basic facts cited from [3] were due to Hrushovski [4]; a full bibliography is in [3]. For general background in stability theory see [1] or [5].

We work at three levels of generality. The first is given by an axiomatic framework in Context 1.10. Section 2 is carried out in this generality. The main family of examples for this context is described in Example 1.3. Sections 3 and 4 depend on a function δ assigning a real number to each finite L-structure as in these examples. Some of the constructions in Section 3 (labeled at the time) use heavily the restriction of the class of examples to graphs. The first author acknowledges useful discussions on this paper with Sergei Starchenko.
Some independence results for control structures in complete numberings
Authors: Jain Sanjay , Nessel Jochen
Published: May 2006

Acceptable programming systems have many nice properties like s-m-n-Theorem, Composition and Kleene Recursion Theorem. Those properties are sometimes called control structures, to emphasize that they yield tools to implement programs in programming systems. It has been studied, among others by Riccardi and Royer, how these control structures influence or even characterize the notion of acceptable programming system. The following is an investigation, how these control structures behave in the more general setting of complete numberings as defined by Mal'cev and Eršov.
On the recursion theorem in iterative operative spaces
Authors: Zashev J.
Published: May 2006

The recursion theorem in abstract partially ordered algebras, such as operative spaces and others, is the most fundamental result of algebraic recursion theory. The primary aim of the present paper is to prove this theorem for iterative operative spaces in full generality. As an intermediate result, a new and rather large class of models of the combinatory logic is obtained.
Definability in low simple theories
Authors: Shami Ziv
Published: May 2006

In 1978 Shelah introduced a new class of theories, called simple (see [Shi]) which properly contained the class of stable theories. Shelah generalized part of the theory of forking to the simple context. After approximately 15 years of neglecting the general theory (although there were works by Hrushovski on finite rank with a definability assumption, as well as deep results on specific simple theories by Cherlin, Hrushovski, Chazidakis, Macintyre and Van den dries, see [CH], [CMV], [HP1], [HP2], [ChH]) there was a breakthrough, initiated with the work of Kim ([K1]). Kim proved that almost all the technical machinery of forking developed in the stable context could be generalized to simple case. However, the theory of multiplicity (i.e., the description of the (bounded) set of non forking extensions of a given complete type) no longer holds in the context of simple theories. Indeed, by contrast to simple theories, stable theories share a strong amalgamation property of types, namely ifpandqare two “free” complete extensions over a superset ofA, and there is no finite equivalence relation overAwhich separates them, then the conjunction ofpandqis consistent (and even free overA.) In [KP] Kim and Pillay proved a weak version of this property for any simple theory, namely “the Independence Theorem for Lascar strong types”. This was a weaker version both because of the requirement that the sets of parameters of the types be mutually independent, as well as the use of Lascar strong types instead of the usual strong types. A very fundamental and interesting problem is whether the independence theorem can be proved for any simple theory, using only the usual strong types. In 1997 Buechler proved ([Bu]) the strong-type version of the independence theorem for an important subclass of simple theories, namely the class of low theories (which includes the class of stable theories and the class of supersimple theories of finite D-rank.)
Topological elementary equivalence of closed semi-algebraic sets in the real plane
Authors: Kuijpers Bart , Paredaens Jan , Van den Bussche Jan
Published: May 2006

We investigate topological properties of subsetsSof the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol forS. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.
Cofinitary groups, almost disjoint and dominating families
Authors: Hrušák Michael , Steprans Juris , Zhang Yi
Published: May 2006

In this paper we show that it is consistent with ZFC that the cardinality of every maximal cofinitary group of Sym(ω) is strictly greater than the cardinal numbers and .
The Modernization of International Law
Authors: Wilson George Grafton
Published: May 2006

Few words have been used with more different meanings than the word “law.” “International law” has likewise had many diverse definitions. The term, international law, is here used to cover the rules and principles which are generally observed in the relations among states. As laws in general become serviceable as their observance becomes regular, so international law becomes serviceable as its rules and principles are generally followed.

The modernization of international law would imply the adaptation of international law to modern conditions. Conditions have changed since the old days when “strange air made a man unfree;” when all foreigners were enemies; when emigration was prohibited lest all man-power of a state might leave and there might be no available material for an army; or when such principles generally prevailed as that of Machiavelli, which he enunciates in the following words: “that whoever is the occasion of another's advancement is the cause of his own diminution” (Chap. 3).

The development of the family of nations idea, and its extension from the Christian European states to other so-called Christian states, and later to states having a recognized political standing, regardless of religious or ethnic bases, shows the enlarging aspects of international relationship. In order that this relationship might continue, it was necessary that principles generally recognized by those having control of political affairs as worthy of their support should underlie these relationships.
Comment on Mr. Corwin's Paper
Authors: Powell Thomas Reed
Published: May 2006

The function of the discusser of a paper is, I take it, like that of Antony at the funeral of Caesar: to bury Corwin, not to praise him. Unfortunately Mr. Corwin has been wanting in the good intentions to pave the way for such a sepulchral performance on my part. He has himself recognized the force of the objections which I would urge to the first half of his paper, had that been all of it, and he has made clear that we cannot tell to what extent constitutional theory is a crutch grabbed to help a wayfarer hobble on to his chosen journey's end, and to what extent it is like a flood or a landslide which sweeps a passive person willy-nilly along its own appointed way. Even worse than this, Mr. Corwin confesses that his game is to indoctrinate his hearers with his own preferred brand of constitutional theory. How can one expose a confidence man who takes us all into his confidence like this? If Mr. Corwin's heart were not as hard as his head, he might have shown more sympathy for his commentator and left him a few soft spots where he might dig in with his intellectual toes.
Sovereign State or Sovereign Group?
Authors: Elliott W. Y.
Published: May 2006

The late Professor William A. Dunning is reported to have said of the recent political theories which attempt to replace the conception of state sovereignty by some pluralistic grouping of social forces, that they were “radically unintelligible.” It is hard for political theorists who have been accustomed to regard the conception of sovereignty as a foundation stone and a sort of “rock of ages” for their faith to be told (as one is every day, more or less) that the anti-intellectualistic type of a sociological basis is the only valid one for juristic structure. For that, according to the old rationalistic conceptions of analytical jurisprudence, is indeed to base sovereignty upon shifting sands and to deprive law of any special significance of its own by equating it with social reactions of the most indeterminate character. But the anti-intellectualistic trend of modern political theory indignantly denies this charge. The assumption, it counters, that any legal center of reference can be final in its authority or in its right to command is an outworn Hegelianism, discredited by practice and theory alike. Law is too much a thing of fictions to be taken seriously in its claims, when it pretends to be giving an accurate description of facts in the abstract terms of a pretended right on the part of the state to be the sole author of enforceable commands and the only rightful claimant of men's ultimate loyalty.
The German Presidential Election
Authors: Graper Elmer D.
Published: May 2006

The recent presidential elections in Germany aroused world-wide interest in spite of the strictly limited constitutional powers of the president. For the first time the German voters were privileged to select the chief executive of the state. The question whether they would turn to some one in sympathy with the pre-war regime or would select an adherent of the Weimar republican constitution was one the answer to which might have important bearings on European politics. Moreover, the personalities of the candidates, especially in the second election, were such as to add to the interest which both Germany's friends and foes felt in the outcome.
Two Forgotten Studies in Political Psychology
Authors: Lasswell Harold D.
Published: May 2006

While it is true that every writer on politics has been to some degree an observer of psychological facts, the significance of this has never been so apparent to systematic students as it is today; otherwise, writings of considerable merit in political psychology could scarcely have suffered the fate of the two books referred to in the present study and have disappeared from sight. Dr. J. G. Zimmerman's Essay on National Pride, published at Zürich in 1758, might very well have been the point of departure for extended research into the nature of patriotism and international attitudes; Gottfried Duden's inquiry, Concerning the Essential Differences of States and the Motives of Human Nature, published at Cologne in 1822, stated problems and suggested methods for the examination of the realities of political power which ought to have inspired a century of minute research. Both books fell flat, and it is only in this day of numerous soundings in psychological politics that it has become worthwhile to disinter them.

That a book about national pride should have been published two years after the beginning of the Seven Years' War is a sharp reminder that European politics had undergone a transformation. The Reformation was undoubtedly a nationalist movement in many of its phases, but it introduced a series of sectional and party disturbances which intercepted the progress of nationalism. These had subsided, and by the eighteenth century the clash of competing imperialisms became not only a basic fact but a fact of which the men of the age were aware.
Choosing Justice: Socrates' Model City and the Practice of Dialectic
Authors: Dobbs Darrell
Published: May 2006

Glaucon's demand to be shown the inherent choiceworthiness of justice exposes the limits of dialectical argument. Acknowledging these limits, Socrates proposes that his interlocutors join him in an alternative activity, making a city in speech. This model city proves to be “entirely opposite” to existing cities, above all (as Socrates observes) because it restricts the practice of dialectical argument to those who first demonstrate a capacity for synopsis, that is, for seeing things as a whole. Socrates holds that one must be able to see things as a whole in order to benefit from the use of dialectic. I interpret the political institutions of Socrates' model city accordingly, as being instrumental to the practice of dialectic. Hence, I reject the prevalent readings of the Republic, which present these institutions either as a blueprint for public policy or as a parody of political idealism. Instead, I suggest that the interlocutors' discussion of censorship, the noble lie, and communism is propaedeutic, fostering the synoptic capacity necessary to benefit from the practice of dialectic, including dialectic aimed at revealing the choiceworthiness of justice.
Thoughtless Assertion and Political Deliberation
Authors: Orlie Melissa A.
Published: May 2006

Predominant views of political deliberation represent it as a matter either of “contemplation without interest” or of interest without contemplation. Whether we claim that political thinking can transcend power or that it is simply a vehicle for it, we abet a nihilistic political culture and authorize the thoughtless exercise of power. What each view denies—or insufficiently explores—is thinking's capacity to transfigure “interest” and power without pretending to transcend them. By contrast, political perspectivism incorporates multiple perspectives in an effort thoughtfully to respond to the will-to-power that attends our location in the world. We need political spaces if we are to become responsive agents of power, because we often can neither recognize the effects of our activities without the benefit of others' perspectives nor alter those effects by our efforts alone.
Linear reasoning. A new form of the Herbrand-Gentzen theorem
Authors: Craig William
Published: May 2006

In Herbrand's Theorem [2] or Gentzen's Extended Hauptsatz [1], a certain relationship is asserted to hold between the structures of A and A′, whenever A implies A′ (i.e., A ⊃ A′ is valid) and moreover A is a conjunction and A′ an alternation of first-order formulas in prenex normal form. Unfortunately, the relationship is described in a roundabout way, by relating A and A′ to a quantifier-free tautology. One purpose of this paper is to provide a description which in certain respects is more direct. Roughly speaking, ascent to A ⊃ A′ from a quantifier-free level will be replaced by movement from A to A′ on the quantificational level. Each movement will be closely related to the ascent it replaces.

The new description makes use of a set L of rules of inference, the L-rules. L is complete in the sense that, if A is a conjunction and A′ an alternation of first-order formulas in prenex normal form, and if A ⊃ A′ is valid, then A′ can be obtained from A by an L-deduction, i.e., by applications of L-rules only. The distinctive feature of L is that each L-rule possesses two characteristics which, especially in combination, are desirable. First, each L-rule yields only conclusions implied by the premisses.
Enumeration of Recursive Sets
Authors: Suzuki Yoshindo
Published: May 2006

It is known [1] p. 312 that a simultaneous enumeration of the recursively enumerable sets can be achieved by a Σ10-predicate. We shall show that a simultaneous enumeration of the recursive sets can be achieved by a predicate of the same form.
On recursively enumerable and arithmetic models of set theory
Authors: Rabin Michael O.
Published: May 2006

In this note we shall prove a certain relative recursiveness lemma concerning countable models of set theory (Lemma 5). From this lemma will follow two results about special types of such models.

Kreisel [5] and Mostowski [6] have shown that certain (finitely axiomatized) systems of set theory, formulated by means of the ϵ relation and certain additional non-logical constants, do not possess recursive models. Their purpose in doing this was to construct consistent sentences without recursive models. As a first corollary of Lemma 5, we obtain a very simple proof, not involving any formal constructions within the system of the notions of truth and satisfiability, of an extension of the Kreisel-Mostowski theorems. Namely, set theory with the single non-logical constant ϵ does not possess any recursively enumerable model. Thus we get, as a side product, an easy example of a consistent sentence containing a single binary relation which does not possess any recursively enumerable model; this sentence being the conjunction of the (finitely many) axioms of set theory.
Finite Axiomatizability using additional predicates
Authors: Craig W. , Vaught R. L.
Published: May 2006

By a theory we shall always mean one of first order, having finitely many non-logical constants. Then for theories with identity (as a logical constant, the theory being closed under deduction in first-order logic with identity), and also likewise for theories without identity, one may distinguish the following three notions of axiomatizability. First, a theory may be recursively axiomatizable, or, as we shall say, simply, axiomatizable. Second, a theory may be finitely axiomatizable using additional predicates (f. a.+), in the syntactical sense introduced by Kleene [9]. Finally, the italicized phrase may also be interpreted semantically. The resulting notion will be called s. f. a.+. It is closely related to the modeltheoretic notion PC introduced by Tarski [16], or rather, more strictly speaking, to PC∩ACδ.

For arbitrary theories with or without identity, it is easily seen that s. f. a.+ implies f. a.+ and it is known that f. a.+ implies axiomatizability. Thus it is natural to ask under what conditions the converse implications hold, since then the notions concerned coincide and one can pass from one to the other.

Kleene [9] has shown: (1) For arbitrary theories without identity, axiomatizability implies f. a.+. It also follows from his work that : (2) For theories with identity which have only infinite models, axiomatizability implies f. a.+.
Sentences true in all constructive models
Authors: Vaught R. L.
Published: May 2006

Let P0, …,Pq be predicates, of which at least one has two or more places. By a formula in P0, …, Pq (or simply a formula, when the list P0, …, Pq is fixed, as in this section) is meant any formula whose only symbols, other than sentential connectives, quantifiers, and (individual) variables, are among P0, …, Pq. A realization (or possible model) of such a formula is a system where A is a non-empty set and each Pk is a relation among the elements of A, having the same number of places as Pk.
Some forms of completeness
Authors: Gilmore P. C.
Published: May 2006

By a theory is meant an applied first-order predicate calculus with at least one predicate symbol and perhaps some individual constants and function symbols and a specified set of axioms. In addition to the terms defined by means of the individual variables, constants, and function symbols a theory may also include among its terms those constructed by means of operators such as the epsilon or iota operators; that is, expressions like (εχΡ) or (οχΡ), where P is a well formed formula (wff) of the theory, may also be terms. A constant term of a theory F is then a term in which no variable occurs free. We are interested only in theories which have at least one constant term so that if a theory doesn't have any individual constants it must necessarily admit as terms expressions constructed by means of operators. A sentence of a theory F is a closed wff.
A propositional calculus with denumerable matrix
Authors: Dummett Michael
Published: May 2006

§1. In [1] Gödel proves the non-existence of a finite matrix characteristic for the intuitionist propositional calculus IC by the use of the finite matrices , where n is a natural number and
Der Prädikatenkalkül mit limitierten variablen Grundlegung einer natürlichen exakten Logik
Authors: Behmann Heinrich
Published: May 2006

1. Überblick

Eine auf neue Art und mit neuen symbolischen Mitteln durchgeführte Analyse des Prozesses der Prädikation ergibt, daβ das für die logisch-mengentheoretischen Paradoxa nach Art des Russellschen essentielle Moment weder das der Selbstprädikation als solches ist noch irgendetwas, was man anderweitig bisher für sie verantwortlich gemacht hat, sondern vielmehr der Umstand, daβ der Algorithmus der Prädikation ebensowohl wie zu einem natürlichen Abschluβ auch auf einen unendlichen Regreβ führen kann. Damit werden die genannten Paradoxa als den bekannten erledigten der mathematischen unendlichen Prozesse wesentlich gleichartig und der gleichen Behandlung zugänglich erkannt. Das neue Kalkülmittel der limitierten Variablen bewirkt – ohne irgendwelche metalogische Regulative ad hoc – die automatische Sicherung des logischen Kalküls gegen die früheren Verführungen.
On Ackermann's set theory
Authors: Lévy Azriel
Published: May 2006

Ackermann introduced in [1] a system of axiomatic set theory. The quantifiers of this set theory range over a universe of objects which we call classes. Among the classes we distinguish the sets. Here we shall show that, in some sense, all the theorems of Ackermann's set theory can be proved in Zermelo-Fraenkel's set theory. We shall also show that, on the other hand, it is possible to prove in Ackermann's set theory very strong theorems of the Zermelo-Fraenkel set theory.
Short-Term Exposure to Fine Particulate Matter and Nitrogen Dioxide and Mortality in 4 Countries
Authors: Ma Yiqun , Nobile Federica , Marb Anne , Dubrow Robert , Stafoggia Massimo , Breitner Susanne , Kinney Patrick L. , Chen Kai
Published: March 2024

Importance

The association between short-term exposure to air pollution and mortality has been widely documented worldwide; however, few studies have applied causal modeling approaches to account for unmeasured confounders that vary across time and space.

Objective

To estimate the association between short-term changes in fine particulate matter (PM2.5) and nitrogen dioxide (NO2) concentrations and changes in daily all-cause mortality rates using a causal modeling approach.

Design, Setting, and Participants

This cross-sectional study used air pollution and mortality data from Jiangsu, China; California; central-southern Italy; and Germany with interactive fixed-effects models to control for both measured and unmeasured spatiotemporal confounders. A total of 8 963 352 deaths in these 4 regions from January 1, 2015, to December 31, 2019, were included in the study. Data were analyzed from June 1, 2021, to October 30, 2023.

Exposure

Day-to-day changes in county- or municipality-level mean PM2.5 and NO2 concentrations.

Main Outcomes and Measures

Day-to-day changes in county- or municipality-level all-cause mortality rates.

Results

Among the 8 963 352 deaths in the 4 study regions, a 10-μg/m3 increase in daily PM2.5 concentration was associated with an increase in daily all-cause deaths per 100 000 people of 0.01 (95% CI, 0.001-0.01) in Jiangsu, 0.03 (95% CI, 0.004-0.05) in California, 0.10 (95% CI, 0.07-0.14) in central-southern Italy, and 0.04 (95% CI, 0.02- 0.05) in Germany. The corresponding increases in mortality rates for a 10-μg/m3 increase in NO2 concentration were 0.04 (95% CI, 0.03-0.05) in Jiangsu, 0.03 (95% CI, 0.01-0.04) in California, 0.10 (95% CI, 0.05-0.15) in central-southern Italy, and 0.05 (95% CI, 0.04-0.06) in Germany. Significant effect modifications by age were observed in all regions, by sex in Germany (eg, 0.05 [95% CI, 0.03-0.06] for females in the single-pollutant model of PM2.5), and by urbanicity in Jiangsu (0.07 [95% CI, 0.04-0.10] for rural counties in the 2-pollutant model of NO2).

Conclusions and Relevance

The findings of this cross-sectional study contribute to the growing body of evidence that increases in short-term exposures to PM2.5 and NO2 may be associated with increases in all-cause mortality rates. The interactive fixed-effects model, which controls for unmeasured spatial and temporal confounders, including unmeasured time-varying confounders in different spatial units, can be used to estimate associations between changes in short-term exposure to air pollution and changes in health outcomes.
Access to High-Resolution Anoscopy Among Persons With HIV and Abnormal Anal Cytology Results
Authors: Rim Sun Hee , Saraiya Mona , Beer Linda , Tie Yunfeng , Yuan Xin , Weiser John
Published: March 2024

This cross-sectional study evaluates use and availability of follow-up anoscopy among persons at highest risk for anal cancer.
Educational Mobility, Pace of Aging, and Lifespan Among Participants in the Framingham Heart Study
Authors: Graf Gloria H. J. , Aiello Allison E. , Caspi Avshalom , Kothari Meeraj , Liu Hexuan , Moffitt Terrie E. , Muennig Peter A. , Ryan Calen P. , Sugden Karen , Belsky Daniel W.
Published: March 2024

Importance

People who complete more education live longer lives with better health. New evidence suggests that these benefits operate through a slowed pace of biological aging. If so, measurements of the pace of biological aging could offer intermediate end points for studies of how interventions to promote education will affect healthy longevity.

Objective

To test the hypothesis that upward educational mobility is associated with a slower pace of biological aging and increased longevity.

Design, Setting, and Participants

This prospective cohort study analyzed data from 3 generations of participants in the Framingham Heart Study: (1) the original cohort, enrolled beginning in 1948; (2) the Offspring cohort, enrolled beginning in 1971; and (3) the Gen3 cohort, enrolled beginning in 2002. A 3-generation database was constructed to quantify intergenerational educational mobility. Mobility data were linked with blood DNA-methylation data collected from the Offspring cohort in 2005 to 2008 (n = 1652) and the Gen3 cohort in 2009 to 2011 (n = 1449). Follow-up is ongoing. Data analysis was conducted from June 2022 to November 2023 using data obtained from the National Institutes of Health database of Genotypes and Phenotypes (dbGaP).

Exposure

Educational mobility was measured by comparing participants’ educational outcomes with those of their parents.

Main Outcomes and Measures

The pace of biological aging was measured from whole-blood DNA-methylation data using the DunedinPACE epigenetic clock. For comparison purposes, the analysis was repeated using 4 other epigenetic clocks. Survival follow-up was conducted through 2019.

Results

This study analyzed data from 3101 participants from the Framingham Heart Study; 1652 were in the Offspring cohort (mean [SD] age, 65.57 [9.22] years; 764 [46.2%] male) and 1449 were in the Gen3 cohort (mean [SD] age, 45.38 [7.83] years; 691 [47.7%] male). Participants who were upwardly mobile in educational terms tended to have slower pace of aging in later life (r = −0.18 [95% CI, −0.23 to −0.13]; P < .001). This pattern of association was similar across generations and held in within-family sibling comparisons. There were 402 Offspring cohort participants who died over the follow-up period. Upward educational mobility was associated with lower mortality risk (hazard ratio, 0.89 [95% CI, 0.81 to 0.98]; P = .01). Slower pace of aging accounted for approximately half of this association.

Conclusions and Relevance

This cohort study’s findings support the hypothesis that interventions to promote educational attainment may slow the pace of biological aging and promote longevity. Epigenetic clocks have potential as near-term outcome measures of intervention effects on healthy aging. Experimental evidence is needed to confirm findings.
Foot and Ankle Care by Podiatrists and Amputations in Patients With Diabetes and Kidney Failure
Authors: Tan Tze-Woei , Caldwell Bryan , Zhang Yi , Kshirsagar Onkar , Cotter Dennis J. , Brewer Thomas W.
Published: March 2024

Importance

Patients with kidney failure have an increased risk of diabetes-related foot complications. The benefit of regular foot and ankle care in this at-risk population is unknown.

Objective

To investigate foot and ankle care by podiatrists and the outcomes of diabetic foot ulcers (DFUs) in patients with kidney failure.

Design, Setting, and Participants

This retrospective cohort study included Medicare beneficiaries with type 2 diabetes receiving dialysis who had a new DFU diagnosis. The analysis of the calendar year 2016 to 2019 data from the United States Renal Data System was performed on June 15, 2023, with subsequent updates on December 11, 2023.

Exposures

Foot and ankle care by podiatrists during 3 months prior to DFU diagnosis.

Main Outcomes and Measures

The outcomes were a composite of death and/or major amputation, as well as major amputation alone. Kaplan-Meier analysis was used to estimate 2 to 3 years of amputation-free survival. Foot and ankle care by podiatrists and the composite outcome was examined using inverse probability-weighted Cox regression, while competing risk regression models were used for the analysis of amputation alone.

Results

Among the 14 935 adult patients with kidney failure and a new DFU (mean [SD] age, 59.3 [12.7] years; 35.4% aged ≥65 years; 8284 men [55.4%]; Asian, 2.7%; Black/African American, 35.0%; Hispanic, 17.7%; White, 58.5%), 18.4% (n = 2736) received care by podiatrists in the 3 months before index DFU diagnosis. These patients were older, more likely to be male, and have more comorbidities than those without prior podiatrist visits. Over a mean (SD) 13.5 (12.0)-month follow-up, 70% of those with podiatric care experienced death and/or major amputation, compared with 74% in the nonpodiatric group. Survival probabilities at 36 months were 26.3% vs 22.8% (P < .001, unadjusted Kaplan-Meier survival analysis). In multivariate regression analysis, foot and ankle care was associated with an 11% lower likelihood of death and/or amputation (hazard ratio [HR], 0.89 95% CI, 0.84-0.93) and a 9% lower likelihood of major amputation (above or below knee) (HR, 0.91; 95% CI, 0.84-0.99) than those who did not.

Conclusions and Relevance

The findings of this study suggest that patients with kidney failure at risk for DFUs who receive foot and ankle care from podiatrists may be associated with a reduced likelihood of diabetes-related amputations.
Role of Ascorbate Peroxidase in Ascorbate‐glutathione Pathway for Stress Tolerance
Authors: Pandey Saurabh , Gupta Kapil , Gupta Kiran , Singh Ravindra P. , Kumar Amit , Gaur Anjali , Panigrahi Jogeswar
Published: March 2024

Under both normal and stressful circumstances, plants produce reactive oxygen species (ROS). However, when environmental conditions are too unfavourable, excessive ROS is produced and the antioxidative defence mechanisms cannot handle the high amounts of ROS, which results in plant damage. The antioxidant defence system's enzymatic and non‐enzymatic components detoxify and scavenge ROS to lessen their harmful effects. The ascorbate‐glutathione (AsA‐GSH) route, also referred to as the Asada‐Halliwell pathway, entails four enzymes that are essential for the detoxification of ROS: AsA peroxidase (APX), dehydroascorbate reductase (DHAR), monodehydroascorbate reductase (MDHAR), and GSH reductase (GR). These enzymes work in conjunction with other plant defence mechanisms in addition to detoxifying ROS to shield plants from different abiotic stress‐related harms. Numerous studies on plants have shown that the up‐regulation or overexpression of these antioxidant enzyme genes enhances the AsA and GSH levels in response to abiotic stresses and helps plants to lower ROS levels. This article outlines the role of APX as a crucial enzyme in the AsA‐GSH pathway and the capacity of plants to withstand abiotic stress.
Expression profiles of four Nile Tilapia innate immune genes during early stages of Aeromonas veronii infection
Authors: Bakry Karima A. , Emeish Walaa F. A. , Embark Hamdy M. , Elkamel Ahmad A. , Mohammed Haitham H.
Published: March 2024

Objective

During Egypt's hot summer season, Aeromonas veronii infection causes catastrophic mortality on Nile Tilapia Oreochromis niloticus farms. Egypt is ranked first in aquaculture production in Africa, sixth in aquaculture production worldwide, and third in global tilapia production. This study aimed to investigate, at the molecular level, the early innate immune responses of Nile Tilapia to experimental A. veronii infection.

Methods

The relative gene expression, co-expression clustering, and correlation of four selected immune genes were studied by quantitative real-time polymerase chain reaction in four organs (spleen, liver, gills, and intestine) for up to 72 h after a waterborne A. veronii challenge. The four genes studied were nucleotide-binding oligomerization domain 1 (NOD1), lipopolysaccharide-binding protein (LBP), natural killer-lysin (NKL), and interleukin-1 beta (IL-1β).

Result

The four genes showed significant transcriptional upregulation in response to infection. At 72 h postchallenge, the highest NOD1 and IL-1β expression levels were recorded in the spleen, whereas the highest LBP and NKL expression levels were found in the gills. Pairwise distances of the data points and the hierarchical relationship showed that NOD1 clustered with IL-1β, whereas LBP clustered with NKL; both genes within each cluster showed a significant positive expression correlation. Tissue clustering indicated that the responses of only the gill and intestine exhibited a significant positive correlation.

Conclusion

The results suggest that NOD1, LBP, NKL, and IL-1β genes play pivotal roles in the early innate immune response of Nile Tilapia to A. veronii infection, and the postinfection expression profile trends of these genes imply tissue-/organ-specific responses and synchronized co-regulation.
A novel AP/PA total body irradiation technique using abutting IMRT fields at extended SSD
Authors: Liang Xiaomin , Li Peixiong , Wu Qiuwen
Published: March 2024

Purpose

To develop a Total Body Irradiation (TBI) technique using IMRT at extended SSD that can be performed in any size Linac room.

Methods

Patients studied were placed on a platform close to the floor, directly under the gantry with cranial‐caudal axis parallel to the gantry rotation plane and at SSD ∼200 cm. Two abutting fields with the same external isocenter at gantry angles of ±21˚, collimator angle of 90˚, and field size of 25 × 40 cm2 are employed for both supine and prone positions. An iterative optimization algorithm was developed to generate a uniform dose at the patient mid‐plane with adequate shielding to critical organs such as lungs and kidneys. The technique was validated in both phantom and patient CT images for treatment planning, and dose measurement and QA were performed in phantom.

Results

A uniform dose distribution in the mid‐plane within ±5% of the prescription dose was reached after a few iterations. This was confirmed with ion‐chamber measurements in phantom. The mean dose to lungs and kidneys can be adjusted according to clinical requirements and can be as low as ∼25% of the prescription dose. For a typical prescription dose of 200 cGy/fraction, the total MU was ∼2400/1200 for the superior/inferior field. The overall treatment time for both supine/prone positions was ∼54 min to meet the maximum absorbed dose rate criteria of 15 cGy/min. IMRT QA with portal dosimetry shows excellent agreement.

Conclusions

We have developed a promising TBI technique using abutting IMRT fields at extended SSD. The patient is in a comfortable recumbent position with good reproducibility and less motion during treatment. An additional benefit of this technique is that full 3D dose distribution is available from the TPS with a DVH summary for organs of interest. The technique allows precise sparing of lungs and kidneys and can be executed in any linac room.
A radiotherapy community data‐driven approach to determine which complexity metrics best predict the impact of atypical TPS beam modeling on clinical dose calculation accuracy
Authors: Brooks Fre'Etta Mae Dayo , Glenn Mallory Carson , Hernandez Victor , Saez Jordi , Mehrens Hunter , Pollard‐Larkin Julianne Marie , Howell Rebecca Maureen , Peterson Christine Burns , Nelson Christopher Lee , Clark Catharine Helen , Kry Stephen Frasier
Published: March 2024

Purpose

To quantify the impact of treatment planning system beam model parameters, based on the actual spread in radiotherapy community data, on clinical treatment plans and determine which complexity metrics best describe the impact beam modeling errors have on dose accuracy.

Methods

Ten beam modeling parameters for a Varian accelerator were modified in RayStation to match radiotherapy community data at the 2.5, 25, 50, 75, and 97.5 percentile levels. These modifications were evaluated on 25 patient cases, including prostate, non‐small cell lung, H&N, brain, and mesothelioma, generating 1,000 plan perturbations. Differences in the mean planned dose to clinical target volumes (CTV) and organs at risk (OAR) were evaluated with respect to the planned dose using the reference (50th‐percentile) parameter values. Correlation between CTV dose differences, and 18 different complexity metrics were evaluated using linear regression; R‐squared values were used to determine the best metric.

Results

Perturbations to MLC offset and transmission parameters demonstrated the greatest changes in dose: up to 5.7% in CTVs and 16.7% for OARs. More complex clinical plans showed greater dose perturbation with atypical beam model parameters. The mean MLC Gap and Tongue & Groove index (TGi) complexity metrics best described the impact of TPS beam modeling variations on clinical dose delivery across all anatomical sites; similar, though not identical, trends between complexity and dose perturbation were observed among all sites.

Conclusion

Extreme values for MLC offset and MLC transmission beam modeling parameters were found to most substantially impact the dose distribution of clinical plans and careful attention should be given to these beam modeling parameters. The mean MLC Gap and TGi complexity metrics were best suited to identifying clinical plans most sensitive to beam modeling errors; this could help provide focus for clinical QA in identifying unacceptable plans.