bluuebunny/crossref_metadata_2025_split huggingface dataset:
Derivate der Zucker‐mercaptale, XXXI. Äthyliden‐ und Isopropylidenverbindungen der 2‐Desoxy‐D‐ribose‐mercaptale
Authors: Zinner Helmut , Schneider Frank 
Published: June 2007

AbstractAus 2‐Desoxy‐D‐ribose‐mercaptalen werden mit Acetaldehyd oder Aceton bei Gegenwart von Kondensationsmitteln 3.5‐Äthyliden‐ bzw. 3.5‐Isopropyliden‐2‐desoxy‐D‐ribose‐mercaptale dargestellt. Ihre Strukturen werden durch Über‐führen in bekannte Verbindungen gesichert.
Untersuchungen über Stilbene, XLVI. Aryläthylenverbindungen des Ferrocens
Authors: Drefahl Günther , Plötner Gerhard , Winnefeld Ilse 
Published: June 2007

AbstractDarstellung und Eigenschaften von Aryläthylenverbindungen des Ferrocens werden beschrieben und die Ergebnisse der UV‐spektroskopischen Untersuchungen diskutiert.
Synthese von Bis‐[2‐amino‐4‐phenyl‐thiazolyl‐(5)]‐methan‐Farbstoffen
Authors: Lässig Wolfgang 
Published: June 2007

AbstractDurch Kondensation von 2‐Amino‐4‐phenyl‐thiazolen mit Formalin werden Bis\[2‐amino‐4‐phenyl‐thiazolyl‐(5)]‐methane erhalten, die zu Bis‐[2‐amino‐4‐phenyl‐thiazolyl‐(5)]‐methan‐Farbstoffen oxydierbar sind.
Über Aromatenkomplexe von Metallen, LXV. Die Isomerenverteilung bei der Friedel‐Crafts‐Acetylierung des π‐Toluol‐chrom‐tricarbonyls und des freien Toluols
Authors: Herberich Gerhard Edwin , Fischer Ernst Otto 
Published: June 2007

AbstractFür die Acetylierung des Toluol‐chrom‐tricarbonyls wurde bei 25° als Isomerenverteilung o:m:p = 39:15:46 gefunden. Eine Deutung – insbesondere des hohen ortho‐Anteils – Wird auf der Grundlage der Bindungstheorie versucht. o‐und p‐ Methyl‐acetophenon‐chrom‐tricarbonyl werden beschrieben. – Zum Vergleich wurde auch Toluol untersucht and entgegen der allgemeinen Auffassung neben p‐Methyl‐acetophenon ∼8% o‐Methyl‐acetophenon nachgewiesen.
Über Orceinfarbstoffe, XVI. Die Autoxydation von Resorcinderivaten, insbesondere des 4.5‐Dimethyl‐resorcins
Authors: Musso Hans , Maassen Dieter 
Published: June 2007

AbstractDie Autoxydationsprodukte von methylsubstituierten Resorcinderivaten zeigen an, daß im Orcein über die bisher isolierten vierzehn Komponenten keine weiteren Phenoxazonfarbstoffe vorkommen. Bei der Autoxydation von 4.5‐Dimethyl‐resorcin in wäßr. Ammoniak entsteht 7‐Hydroxy‐3.4.5.6‐tetramethyl‐phenoxazon‐(2).
Über Orceinfarbstoffe, XVII. Die Autoxydation des 4.5.6‐Trimethyl‐resorcins
Authors: Musso Hans , Maassen Dieter , Bormann Dieter 
Published: June 2007

Abstract4.5.6‐Trimethyl‐resorcin reagiert in alkalischer Lösung mit Luftsauerstoff in guter Ausbeute zum Trimethylchinol II, dessen drei tautomere Formen spektroskopisch in Lösung nachgewiesen werden. Eindeutige Synthesen für dieses Chinol und Trimethyl‐pyrogallol werden mitgeteilt.
Die ω‐Phenylierung von Perchlor‐pentadien‐(1.3)‐säure‐(5)‐chlorid
Authors: Roedig Alfred , Märkl Gottfried , Schaal Victor 
Published: June 2007

AbstractDie AlCl3‐katalysierte Reaktion von Perchlor‐pentadien‐(1.3)‐säure‐(5)‐chlorid mit Benzol führt zu einer Verbindung, die alle typischen Eigenschaften eines Carbonsäurechlorids zeigt. Für sie wird die Konstitution des 1.2.3.4‐Tetrachlor‐1‐phenyl‐pentadien‐(1.3)‐säure‐(5)‐chlorids bewiesen. Demnach hat entweder eine Umlagerung eines primär gebildeten Ketons im Verlaufe der Friedel‐Crafts‐Reaktion stattgefunden, oder es könnte das Perchlor‐pentadiensäurechlorid in Form des tautomeren Perchlor‐pyryliumchlorids in eine direkte elektrophile Substitution mit dem Benzol eingetreten sein.
Ringschlußreaktionen mit Tetrachlor‐1‐phenyl‐pentadien‐(1.3)‐säure‐(5)‐chlorid
Authors: Märkl Gottfried , Roedig Alfred , Schaal Victor 
Published: June 2007

AbstractTetrachlor‐1‐phenyl‐pentadien‐(1.3)‐säure‐(5)‐chlorid wird durch Aluminiumchlorid bereits bei Raumtemperatur zu Pentachlor‐2‐phenyl‐cyclopenten‐(1)‐on‐(3) isomerisiert. Mit Phosphorpentachlorid erfährt es bei 150° einen Naphthalinringschluß. Die Konstitution der Cyclisierungsprodukte wird auf chemischem Wege sowie durch Vergleich von UV‐ und IR‐Spektren beweisen.
Oligosaccharidsynthesen, IV. Synthesen α‐ und β‐konfigurierter Disaccharide
Authors: Bredereck Hellmut , Wagner Adolf , Geissel Dieter , Ott Hermann 
Published: June 2007

AbstractBei der Umsetzung von Tritylzuckern mit 2‐Trichloracetyl‐triacetyl‐glucopyranosyl‐chlorid in Gegenwart von Silberperchlorat erhält man trennbare Gemische von α‐und β‐konfigurierten Disacchariden im Verhältnis 1:1.
Über die Einwirkung von Schwefelkohlenstoff auf Diaryldiazomethane und Ylide. Bildung von 1.2.4.5‐Tetrathia‐cyclohexanen und dimerer Thioketene
Authors: Schönberg Alexander , Frese Emil , Brosowski Karl‐Heinz 
Published: June 2007

AbstractDie Einwirkung von Schwefelkohlenstoff auf Diaryldiazomethane führt zur Bildung von 3.6‐Dimethylen‐1.2.4.5‐tetrathia‐cyclohexanen (vgl. u. a. VI), die mit Kupferpulver 2.4‐Dimethylen‐1.3‐dithia‐cyclobutane (vgl. u. a. VII) liefern. Letztere entstehen auch aus Schwefelkohlenstoff und Phosphor‐yliden (vgl. u. a. XIVa → IX). Die Dimethylen‐1.3‐dithia‐cyclobutane sind als dimere Thioketene aufzufassen, ihre sehr große Thermostabilität wird durch das ”︁Gewicht„ polarer Grenzstrukturen erklärt, entsprechendes gilt von den Desaurinen.
Jump Theorems for REA Operators
Authors: Lachlan Alistair H. , Yi Xiaoding 
Published: June 2007

AbstractIn [2], Jockusch and Shore have introduced a new hierarchy of sets and operators called the REA hierarchy. In this note we prove analogues of the Friedberg Jump Theorem and the Sacks Jump Theorem for many REA operators. MSC: 03D25, 03D55.
On a duality between Boolean valued analysis and topological Reduction Theory
Authors: Nishimura Hirokazu 
Published: June 2007

AbstractBy creating an unbounded topological reduction theory for complex Hilbert spaces over Stonean spaces, we can give a category‐theoretic duality between Boolean valued analysis and topological reduction theory for complex Hilbert spaces. MSC: 03C90, 03E40, 06E15, 46M99.
A variant of the Notion of Semicreative set
Authors: Rolletschek Heinrich 
Published: June 2007

AbstractThis paper introduces the notion of cW10‐creative set, which strengthens that of semicreative set in a similar way as complete creativity strengthens creativity. Two results are proven, both of which imply that not all semicreative sets are cW10‐creative. First, it is shown that semicreative Dedekind cuts cannot be cW10‐creative; the existence of semicreative Dedekind cuts was shown by Soare. Secondly, it is shown that (i) if A ⊕ B, the join of A and B, is cW10‐creative, then either A or B is cW10‐creative, and (ii) the same is not true with ‘cW10‐creative’ replaced by ‘semicreative’. Moreover, sets A, B which provide a counterexample for (ii) can be constructed within any given nonrecursive r.e. T‐degrees a, b. MSC: 03D30.
Sequential, pointwise, and uniform continuity: A constructive note
Authors: Bridges Douglas S. 
Published: June 2007

AbstractThe main result of this paper is a weak constructive version of the uniform continuity theorem for pointwise continuous, real‐valued functions on a convex subset of a normed linear space. Recursive examples are given to show that the hypotheses of this theorem are necessary. The remainder of the paper discusses conditions which ensure that a sequentially continuous function is continuous. MSC: 03F60, 26E40, 46S30.
Remarks on Levy's reflection axiom
Authors: Dowd Martin 
Published: June 2007

AbstractAdding higher types to set theory differs from adding inaccessible cardinals, in that higher type arguments apply to all sets rather than just ordinary ones. Levy's reflection axiom is justified, by considering the principle that we can pretend that the universe is a set, together with methods of Gaifman [8]. We reprove some results of Gaifman, and some facts about Levy's reflection axiom, including the fact that adding higher types yields no new theorems about sets. Some remarks on standard models are made. An obvious strengthening of Levy's axiom to higher types is considered, which implies the existence of indescribable cardinals. Other remarks about larger cardinals are made; some questions of Gloede [9] are settled. Finally we argue that the evidence for V = L is strong, and that CH is certainly true. MSC: 03E30, 03E55.
On roots of exponential terms
Authors: Wolter Helmut 
Published: June 2007

AbstractIn the present paper some tools are given to state the exact number of roots for some simple classes of exponential terms (with one variable). The result were obtained by generalizing Sturm's technique for real closed fields. Moreover for arbitrary non‐zero terms t(x) certain estimations concerning the location of roots of t(x) are given. MSC: 03C65, 03C60, 12L12.
Normal form of derivations in the nonassociative and commutative lambek calculus with product
Authors: Kandulski Maciej 
Published: June 2007

AbstractWe show that derivations in the nonassociative and commutative Lambek calculus with product can be transformed to a normal form as it is the case with derivations in noncommutative calculi. As an application we obtain that the class of languages generated by categorial grammars based on the nonassociative and commutative Lambek calculus with product is included in the class of CF‐languages. MSC: 68Q50, 03D15, 03B65.
The finite cutset property
Authors: Brochet J.‐M. 
Published: June 2007

AbstractA cutset of H is a subset of ∪ H which meets every element of H. H has the finite cutset property if every cutset of H contains a finite one. We study this notion, and in particular how it is related to the compactness of H for the natural topology. MSC: 04A20, 54D30.
Classically complete modal relevant logics
Authors: Mares Edwin D. 
Published: June 2007

AbstractA variety of modal logics based on the relevant logic R are presented. Models are given for each of these logics and completeness is shown. It is also shown that each of these logics admits Ackermann's rule γ and as a corollary of this it is proved that each logic is a conservative extension of its counterpart based on classical logic, hence we call them “classically complete”. MSC: 03B45, 03B46.
Local computation in linear logic
Authors: Solitro Ugo , Valentini Silvio 
Published: June 2007

AbstractThis work deals with the exponential fragment of Girard's linear logic ([3]) without the contraction rule, a logical system which has a natural relation with the direct logic ([10], [7]). A new sequent calculus for this logic is presented in order to remove the weakening rule and recover its behavior via a special treatment of the propositional constants, so that the process of cut‐elimination can be performed using only “local” reductions. Hence a typed calculus, which admits only local rewriting rules, can be introduced in a natural manner. Its main properties — normalizability and confluence — has been investigated; moreover this calculus has been proved to satisfy a Curry‐Howard isomorphism ([6]) with respect to the logical system in question. MSC: 03B40, 03F05.
Open subspaces of locally compact metric spaces
Authors: Mandelkern Mark 
Published: June 2007

AbstractAlthough classically every open subspace of a locally compact space is also locally compact, constructively this is not generally true. This paper provides a locally compact remetrization for an open set in a compact metric space and constructs a one‐point compactification. MSC: 54D45, 03F60, 03F65.
Higher type categories
Authors: Dowd Martin 
Published: June 2007

AbstractHigher types can readily be added to set theory, Bernays‐Morse set theory being an example. A type for each ordinal is added in [2]. Adding higher types to set theory provides a neat solution to the problem of how to handle higher type categories. We give the basic definitions, and prove cocompleteness of some higher type categories. MSC: 14A15.
A simplified functorial construction of the veblen hierarchy
Authors: Weiermann Andreas 
Published: June 2007

AbstractWe give a simple and elementary proof of the following result of Girard and Vauzeilles which is proved in [5]: “The binary Veblen function ψ: On × On — On is a dilator.” Our proof indicates the intimate connection between the traditional theory of ordinal notation systems and Girard's theory of denotation systems. MSC: 03F15.
A partial model of NF with ZF
Authors: Prati Nando 
Published: June 2007

AbstractThe theory New Foundations (NF) of Quine was introduced in [14]. This theory is finitely axiomatizable as it has been proved in [9]. A similar result is shown in [8] using a system called K. Particular subsystems of NF, inspired by [8] and [9], have models in ZF. Very little is known about subsystems of NF satisfying typical properties of ZF; for example in [11] it is shown that the existence of some sets which appear naturally in ZF is an axiom independent from NF (see also [12]). Here we discuss a model of subsystems of NF in which there is a set which is a model of ZF. MSC: 03E70.
The theorem of the means for cardinal and ordinal numbers
Authors: Rousseau George 
Published: June 2007

AbstractThe theorem that the arithmetic mean is greater than or equal to the geometric mean is investigated for cardinal and ordinal numbers. It is shown that whereas the theorem of the means can be proved for n pairwise comparable cardinal numbers without the axiom of choice, the inequality a2 + b2 ≥ 2ab is equivalent to the axiom of choice. For ordinal numbers, the inequality α2 + β2 ≥ 2αβ is established and the conditions for equality are derived; stronger inequalities are obtained for finite and infinite sequences of ordinals under suitable monotonicity hypotheses. MSC: 03E10, 04A10, 03E25, 04A25.
Hierarchies of Partially Ordered Connectives and Quantifiers
Authors: Krynicki Michał 
Published: June 2007

AbstractConnections between partially ordered connectives and Henkin quantifiers are considered. It is proved that the logic with all partially ordered connectives and the logic with all Henkin quantifiers coincide. This implies that the hierarchy of partially ordered connectives is strongly hierarchical and gives several nondefinability results between some of them. It is also deduced that each Henkin quantifier can be defined by a quantifier of the form

what is a strengthening of the Walkoe result. MSC: 03C80.
Constructive notions of strict convexity
Authors: Bridges Douglas S. 
Published: June 2007

AbstractTwo classically equivalent, but constructively inequivalent, strict convexity properties of a preference relation are discussed, and conditions given under which the stronger notion is a consequence of the weaker. The last part of the paper introduces uniformly rotund preferences, and shows that uniform rotundity implies strict convexity. The paper is written from a strictly constructive point of view, in which all proofs embody algorithms. MSC: 03F60, 90A06.
Prefinitely axiomatizable modal and intermediate logics
Authors: Kracht Marcus 
Published: June 2007

AbstractA logic Λ bounds a property P if all proper extensions of Λ have P while Λ itself does not. We construct logics bounding finite axiomatizability and logics bounding finite model property in the lattice of intermediate logics and in the lattice of normal extensions of K4.3. MSC: 03B45, 03B55.
Hilbert's ϵ‐operator in intuitionistic type theories
Authors: Bell John L. 
Published: June 2007

AbstractWe investigate Hilbert's ϵ‐calculus in the context of intuitionistic type theories, that is, within certain systems of intuitionistic higher‐order logic. We determine the additional deductive strength conferred on an intuitionistic type theory by the adjunction of closed ϵ‐terms. We extend the usual topos semantics for type theories to the ϵ‐operator and prove a completeness theorem. The paper also contains a discussion of the concept of “partially defined” ϵ‐term. MSC: 03B15, 03B20, 03G30.
System function languages
Authors: Thuraisingham M. B. 
Published: June 2007

AbstractIn this paper we define the concept of a system function language which is a language generated by a system function. We identify system function languages with recursively enumerable sets which are non‐simple and co‐infinite. We then define restricted system function languages and identify them with recursive sets which are co‐infinite. Finally we state and prove some independence and dependence relationships between system function languages and some of the more well‐known decision problems. MSC: 03D05, 03D20, 03D25.
On Preservation of Stability for Finite Extensions of Abelian Groups
Authors: Haug Frieder 
Published: June 2007

AbstractWe characterize preservation of superstability and ω‐stability for finite extensions of abelian groups and reduce the general case to the case of p‐groups. In particular we study finite extensions of divisible abelian groups. We prove that superstable abelian‐by‐finite groups have only finitely many conjugacy classes of Sylow p‐subgroups.Mathematics Subject Classification: 03C60, 20C05.
Fregean Extensions of First‐Order Theories
Authors: Bell John L. 
Published: June 2007

AbstractIt is shown by Parsons [2] that the first‐order fragment of Frege's (inconsistent) logical system in the Grundgesetze der Arithmetic is consistent. In this note we formulate and prove a stronger version of this result for arbitrary first‐order theories. We also show that a natural attempt to further strengthen our result runs afoul of Tarski's theorem on the undefinability of truth.Mathematics Subject Classification: 03B10.
An Application of Logic to Combinatorial Geometry: How Many Tetrahedra are Equidecomposable with a Cube?
Authors: Kreinovich Vladik , Kosheleva Olga 
Published: June 2007

AbstractIt is known (see Rapp [9]) that elementary geometry with the additional quantifier “there exist uncountably many” is decidable. We show that this decidability helps in solving the following problem from combinatorial geometry: does there exist an uncountable family of pairwise non‐congruent tetrahedra that are n‐equidecomposable with a cube?Mathematics Subject Classification: 03B25, 03C80, 51M04, 52B05, 52B10.
Complements of Intersections in Constructive Mathematics
Authors: Bridges Douglas S. , Ishihara Hajime 
Published: June 2007

AbstractWe examine, from a constructive perspective, the relation between the complements of S, T, and S ∩ T in X, where X is either a metric space or a normed linear space. The fundamental question addressed is: If x is distinct from each element of S ∩ T, if s ϵ S, and if t ϵ T, is x distinct from s or from t? Although the classical answer to this question is trivially affirmative, constructive answers involve Markov's principle and the completeness of metric spaces.Mathematics Subject Classification: 03F65, 46S30.
Translations of Logical Formulas and the Equiconsistency Problem
Authors: Kuzichev Andrei A. 
Published: June 2007

AbstractA translation of formulas in a language L1 to formulas in a language L2 is a mapping which preserves the parameters and commutes with the substitution prefix, the propositional connectives and the quantifiers. Every translation generates a corresponding transformation of theories in L1 to theories in L2. We formulate the equiconsistency problem for such transformations and propose a variant of its solution. First, for a transformation F we find the least theory A(F) in L1 such that its inclusion in a theory T (in L1) guarantees equiconsistency of F and F(T), then we propose axiomatizations of A(F) for some F's.Mathematics Subject Classification: 03B10, 03B15, 03F25.
A Finite Hilbert‐Style Axiomatization of the Implication‐Less Fragment of the Intuitionistic Propositional Calculus
Authors: Rebagliato Jordi , Verdú Ventura 
Published: June 2007

AbstractIn this paper we obtain a finite Hilbert‐style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}‐formulas containing this fragment.Mathematics Subject Classification: 03B20, 03B22, 06D15.
Boolean Valued and Stone Algebra Valued Measure Theories
Authors: Nishimura Hirokazu 
Published: June 2007

AbstractIn conventional generalization of the main results of classical measure theory to Stone algebra valued measures, the values that measures and functions can take are Booleanized, while the classical notion of a σ‐field is retained. The main purpose of this paper is to show by abundace of illustrations that if we agree to Booleanize the notion of a σ‐field as well, then all the glorious legacy of classical measure theory is preserved completely.Mathematics Subject Classification: 03C90, 28B15.
Ternary Operations as Primitive Notions for Constructive Plane Geometry IV
Authors: Pambuccian Victor 
Published: June 2007

AbstractIn this paper we provide a quantifier‐free constructive axiomatization for Euclidean planes in a first‐order language with only ternary operation symbols and three constant symbols (to be interpreted as ‘points’). We also determine the algorithmic theories of some ‘naturally occurring’ plane geometries.Mathematics Subject Classification: 03F65, 51M05, 51M15, 03B30.
The Index Set of Injectively Enumerable Classes of Recursively Enumerable Sets in ∑5‐Complete
Authors: Wehner Stephan 
Published: June 2007

AbstractI introduce an effective enumeration of all effective enumerations of classes of r. e. sets and define with this the index set IE of injectively enumerable classes. It is easy to see that this set is ∑5 in the Arithmetical Hierarchy and I describe a proof for the ∑5‐hardness of IE.Mathematics Subject Classification: 03D25, 03D45.
Acceptable Numerations of Morphisms and Myhill‐Shepherdson Property
Authors: Kanda Akira 
Published: June 2007

AbstractMyhill‐Shepherdson property in recursive function theory states that extensional effective program transformations determine continuous operations on partial functions. Case showed that this property fails to characterize acceptability of numberings of partial recursive functions. In this note we present a higher type analogue to Myhill‐Shepherdson property. Our purpose is to show that higher type Myhill‐Shepherdson property characterizes weak acceptability under a natural condition.
Some Connections between Topological and Modal Logic
Authors: Engesser Kurt 
Published: June 2007

AbstractWe study modal logics based on neighbourhood semantics using methods and theorems having their origin in topological model theory. We thus obtain general results concerning completeness of modal logics based on neighbourhood semantics as well as the relationship between neighbourhood and Kripke semantics. We also give a new proof for a known interpolation result of modal logic using an interpolation theorem of topological model theory.
On Σ1‐definable Functions Provably Total in I ∏
Authors: Bigorajska Teresa 
Published: June 2007

AbstractWe prove the following theorem: Let φ(x) be a formula in the language of the theory PA− of discretely ordered commutative rings with unit of the form ∃yφ′(x,y) with φ′ and let ∈ Δ0 and let fφ: ℕ → ℕ such that fφ(x) = y iff φ′(x,y) & (∀z < y) φ′(x,z). If I ∏ ∈(∀x ≥ 0), φ then there exists a natural number K such that I ∏ ⊢ ∃y∀x(x > y ⟹ ƒφ(x) < xK). Here I ∏1− denotes the theory PA− plus the scheme of induction for formulas φ(x) of the form ∀yφ′(x,y) (with φ′) with φ′ ∈ Δ0.
Automorphisms of Countable Recursively Saturated Models of PA: Open Subgroups and Invariant Cuts
Authors: Kotlarski Henryk , Piekart Bozena 
Published: June 2007

AbstractLetMbe a countable recursively saturated model of PA andHan open subgroup ofG= Aut(M). We prove thatI(H)= sup {b ∈M: (∃ƒ ∈G\H) ∀u<bfu=uandJ(H)= inf{b ∈MH} may be invariant, i. e. fixed by all automorphisms ofM.