bluuebunny/crossref_metadata_2025 huggingface dataset:
Complexity of interpolation and related problems in positive calculi
Authors: Maksimova Larisa
Published: December 2007

We consider the problem of recognizing important properties of logical calculi and find complexity bounds for some decidable properties. For a given logical systemL, a property P of logical calculi is called decidable overLif there is an algorithm which for any finite setAxof new axiom schemes decides whether the calculusL+Axhas the property P or not. In [11] the complexity of tabularity, pre-tabularity. and interpolation problems over the intuitionistic logic Int and over modal logic S4 was studied, also we found the complexity of amalgamation problems in varieties of Heyting algebras and closure algebras.

In the present paper we deal with positive calculi. We prove NP-completeness of tabularity, DP-hardness of pretabularity and PSPACE-completeness of interpolation problem over Int+. In addition to above-mentioned properties, we consider Beth's definability properties. Also we improve some complexity bounds for properties of superintuitionistic calculi.
Pfaffian differential equations over exponential o-minimal structures
Authors: Miller Chris , Speissegger Patrick
Published: December 2007

In this paper, we continue investigations into the asymptotic behavior of solutions of differential equations over o-minimal structures.

Let ℜ be an expansion of the real field (ℝ, +, ·).

A differentiable mapF= (F1,…,F1): (a, b) → ℝiisℜ-Pfaffianif there existsG: ℝ1+l→ ℝldefinable in ℜ such thatF′(t) =G(t, F(t)) for allt∈ (a, b) and each component functionGi: ℝ1+l→ ℝ is independent of the lastl−ivariables (i= 1, …,l). If ℜ is o-minimal andF: (a, b) → ℝlis ℜ-Pfaffian, then (ℜ,F) is o-minimal (Proposition 7). We say thatF: ℝ → ℝlis ultimately ℜ-Pfaffian if there existsr∈ ℝ such that the restrictionF↾(r, ∞) is ℜ-Pfaffian. (In general,ultimatelyabbreviates “for all sufficiently large positive arguments”.)

The structure ℜ isclosed under asymptotic integrationif for each ultimately non-zero unary (that is, ℝ → ℝ) functionfdefinable in ℜ there is an ultimately differentiable unary functiongdefinable in ℜ such that limt→+∞[g′(t)/f(t)] = 1- If ℜ is closed under asymptotic integration, then ℜ is o-minimal and definesex: ℝ → ℝ (Proposition 2).

Note that the above definitions make sense for expansions of arbitrary ordered fields.
Congruence relations on lattices of recursively enumerable sets
Authors: Hammond Todd
Published: December 2007

Let {We}e∈ω be a standard enumeration of the recursively enumerable (r. e.) subsets of ω = {0, 1, 2, …}. The lattice of recursively enumerable sets, is the structure ({We}e∈ω, ∪, ∩). is the sublattice of consisting of the recursive sets.

Suppose is a lattice of subsets of ω. ≡ is said to be a congruence relation on if ≡ is an equivalence relation on and if for all U, U′ ∈ and V, V ∈ , if U ≡ U′ and V ≡ V′ then U ∪ U′ ≡ V ∪ V′ and U ∩ U′ ≡ V ∩ V′. [U] = {V ∈ | V ≡ U} is the equivalence class of U. If ≡ is a congruence relation on , the elements of the quotient lattice / ≡ are the equivalence classes of ≡. [U] ∪ [V] is defined as [U ∪ V], and [U] ∩ [V] is defined as [U ∩ V].

The quotient lattices of (or of some sublattice ) correspond naturally with the congruence relations which give rise to them, and in turn the congruence relations of sublattices of can be characterized in part by their computational complexity. The aim of the present paper is to characterize congruence relations in some of the most important complexity classes.
Monoid based semantics for linear formulas (corrected republication)
Authors: Mitchell W. P. R. , Simmons H.
Published: December 2007

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of handling duality.
Splitting properties of n-c.e. enumeration degrees
Authors: Kalimullin I. SH.
Published: December 2007

It is proved that if 1 < m < 2p ≤ n for some integer p then the elementary theories of posets of m-c.e. and n-c.e. e-degrees are distinct. It is proved also that the structures 〈2n, ≤, 〉 and 〈2n, ≤. P〉 are not elementary equivalent where P is the predicate P(a) = “a is a e-degree”.
Groundwork for weak analysis
Authors: Fernandes António M. , Ferreira Fernando
Published: December 2007

This paper develops the very basic notions of analysis in a weak second-order theory of arithmetic BTFA whose provably total functions are the polynomial time computable functions. We formalize within BTFA the real number system and the notion of a continuous real function of a real variable. The theory BTFA is able to prove the intermediate value theorem, wherefore it follows that the system of real numbers is a real closed ordered field. In the last section of the paper, we show how to interpret the theory BTFA in Robinson's theory of arithmetic Q. This fact entails that the elementary theory of the real closed ordered fields is interpretable in Q.
Coding with ladders a well ordering of the reals
Authors: Abraham Uri , Shelah Saharon
Published: December 2007

Any model of ZFC + GCH has a generic extension (made with a poset of size ℵ2) in which the following hold: there exists a-well ordering of the reals, The proof consists in iterating posets designed to change at will the guessing properties of ladder systems on ω1. Therefore, the study of such ladders is a main concern of this article.
An isomorphism between monoids of external embeddings: About definability in arithmetic
Authors: Prunescu Mihai
Published: December 2007

We use a new version of the Definability Theorem of Beth in order to unify classical theorems of Yuri Matiyasevich and Jan Denef in one structural statement. We give similar forms for other important definability results from Arithmetic and Number Theory.
Interpolation for first order S5
Authors: Fitting Melvin
Published: December 2007

An interpolation theorem holds for many standard modal logics, but first order S5 is a prominent example of a logic for which it fails. In this paper it is shown that a first order S5 interpolation theorem can be proved provided the logic is extended to contain propositional quantifiers. A proper statement of the result involves some subtleties, but this is the essence of it.
Multiplication complexe et équivalence élémentaire dans le langage des corps (Complex multiplication and elementary equivalence in the language of fields)
Authors: Vidaux Xavier
Published: December 2007

Let K and K′ be two elliptic fields with complex multiplication over an algebraically closed field k of characteristic 0. non k-isomorphic, and let C and C′ be two curves with respectively K and K′ as function fields. We prove that if the endomorphism rings of the curves are not isomorphic then K and K′ are not elementarily equivalent in the language of fields expanded with a constant symbol (the modular invariant). This theorem is an analogue of a theorem from David A. Pierce in the language of k-algebras.
On orbits, of prompt and low computably enumerable sets
Authors: Wald Kevin
Published: December 2007

This paper concerns automorphisms of the computably enumerable sets. We prove two results relating semilow sets and prompt degrees via automorphisms, one of which is complementary to a recent result of Downey and Harrington. We also show that the property of effective simplicity is not invariant under automorphism, and that in fact every promptly simple set is automorphic to an effectively simple set. A major technique used in these proofs is a modification of the Harrington-Soare version of the method of Harrington-Soare and Cholak for constructing Δ30 automorphisms; this modification takes advantage of a recent result of Soare on the extension of “restricted” automorphisms to full automorphisms.
Definable incompleteness and Friedberg splittings
Authors: Miller Russell
Published: December 2007

We define a property R(A0, A1) in the partial order of computably enumerable sets under inclusion, and prove that R implies that A0 is noncomputable and incomplete. Moreover, the property is nonvacuous. and the A0 and A1 which we build satisfying R form a Friedberg splitting of their union A, with A1 prompt and A promptly simple. We conclude that A0 and A1 lie in distinct orbits under automorphisms of , yielding a strong answer to a question previously explored by Downey, Stob, and Soare about whether halves of Friedberg splittings must lie in the same orbit.
On Dipphantine definability and decidability in some rings of algebraic functions of characteristic 0
Authors: Shlapentokh Alexandra
Published: December 2007

LetKbe a function field of one variable over a constant fieldCof finite transcendence degree over ℂ. LetM/Kbe a finite extension and letWbe a set of primes ofKsuch that all but finitely many primes ofWdo not split in the extensionM/K. Then there exists a setW′ofK-primes such that Hilbert's Tenth Problem is not decidable overOK,W′= {xϵK∣ordþx≥ 0, ∀þ ∉W′}, and the set (W′ ∖W)∪{W∖W′) is finite.

LetKbe a function field of one variable over a constant fieldCfinitely generated over ℚ. LetM/Kbe a finite extension and letWbe a set of primes ofKsuch that all but finitely many primes ofWdo not split in the extensionM/Kand the degree of all the primes inWis bounded bybϵ ℕ. Then there exists a setW′ ofK-primes such that ℤ has a Diophantine definition overOK,W′, and the set (W′ ∖W)∪(W∖W′) is finite.
Generalised weak presentations
Authors: Shlapentokh Alexandra
Published: December 2007

Let K be a computable field. Let ℱ be a collection of recursive functions over K, possibly including field operations. We investigate the following question. Given an r.e. degree . is there an injective map j : K → ℕ such that j(K) is of degree a and all the functions in ℱ are translated by restrictions of total recursive functions.
Indestructibility and the level-by-level agreement between strong compactness and supercompactness
Authors: Apter Arthur W. , Hamkins Joel David
Published: December 2007

Can a supercompact cardinal κ be Laver indestructible when there is a level-by-level agreement between strong compactness and supercompactness? In this article, we show that if there is a sufficiently large cardinal above κ, then no, it cannot. Conversely, if one weakens the requirement either by demanding less indestructibility, such as requiring only indestructibility by stratified posets. or less level-by-level agreement, such as requiring it only on measure one sets, then yes. it can.
Some results on permutation group isomorphism and categoricity
Authors: Pillay Anand , Schlatter Mark D.
Published: December 2007

We extend Morley's Theorem to show that if a theory is κ-p-categorical for some uncountable cardinal κ, it is uncountably categorical. We then discuss ω-p-categoricity and provide examples to show that similar extensions for the Baldwin-Lachlan and Lachlan Theorems are not possible.
Properties of forking in ω-free pseudo-algebraically closed fields
Authors: Chatzidakis Zoé
Published: December 2007

The study of pseudo-algebraically closed fields (henceforth called PAC) started with the work of J. Ax on finite and pseudo-finite fields [1]. He showed that the infinite models of the theory of finite fields are exactly the perfect PAC fields with absolute Galois group isomorphic to , and gave elementary invariants for their first order theory, thereby proving the decidability of the theory of finite fields. Ax's results were then extended to a larger class of PAC fields by M. Jarden and U. Kiehne [21], and Jarden [19]. The final word on theories of PAC fields was given by G. Cherlin, L. van den Dries and A. Macintyre [10], see also results by Ju. Ershov [13], [14]. Let K be a PAC field. Then the elementary theory of K is entirely determined by the following data:

• The isomorphism type of the field of absolute numbers of K (the subfield of K of elements algebraic over the prime field).

• The degree of imperfection of K.

• The first-order theory, in a suitable ω-sorted language, of the inverse system of Galois groups al(L/K) where L runs over all finite Galois extensions of K.

They also showed that the theory of PAC fields is undecidable, by showing that any graph can be encoded in the absolute Galois group of some PAC field. It turns out that the absolute Galois group controls much of the behaviour of the PAC fields. I will give below some examples illustrating this phenomenon.
The theory of modules of separably closed fields 1
Authors: Dellunde Pilar , Delon Françoise , Point Françoise
Published: December 2007

We consider separably closed fields of characteristic p > 0 and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the p-component functions.
On the binding group in simple theories
Authors: Shami Ziv , Wagner Frank O.
Published: December 2007

We show that ifpis a real type which is almost internal in a formula φ in a simple theory, then there is a typep′ interalgebraic with a finite tuple of realizations ofp, which is generated overφ. Moreover, the group of elementary permutations ofp′ over all realizations ofφis type-definable.
Generic variations of models ofT
Authors: Baudisch Andreas
Published: December 2007

LetTbe a model-complete theory that eliminates the quantifier ∃∞xForTwe construct a theoryT+such that any element in a model ofT+determines a model ofT. We show thatT+has a model companionT1. We can iterate the construction. The produced theories are investigated.
Isolation and lattice embeddings
Authors: Wu Guohua
Published: December 2007

Say that (a, d) is an isolation pair if a is a c.e. degree, d is a d.c.e. degree, a < d and a bounds all c.e. degrees below d. We prove that there are an isolation pair (a, d) and a c.e. degree c such that c is incomparable with a, d, and c cups d to o′, caps a to o. Thus, {o, c, d, o′} is a diamond embedding, which was first proved by Downey in [9]. Furthermore, combined with Harrington-Soare continuity of capping degrees, our result gives an alternative proof of N5 embedding.
Generalized r-cohesiveness and the arithmetical hierarchy: a correction to “Generalized cohesiveness”
Authors: Jockusch Carl G. , Lakins Tamara J.
Published: December 2007

For X ⊆ ω, let [X]n denote the class of all n-element subsets of X. An infinite set A ⊆ ω is called n-r-cohesive if for each computable function f: [ω]n → {0, 1} there is a finite set F such that f is constant on [A − F]n. We show that for each n > 2 there is no Πn0 set A ⊆ ω which is n-r-cohesive. For n = 2 this refutes a result previously claimed by the authors, and for n ≥ 3 it answers a question raised by the authors.
Strong convergence in finite model theory
Authors: Lotfallah Wafik Boulos
Published: December 2007

In [9] we introduced a new framework for asymptotic probabilities, in which a σ-additive measure is defined on the sample space of all sequences of finite models, where the universe of , is {1,2,…,n}. In this framework we investigated the strong 0-1 law for sentences, which states that each sentence either holds in eventually almost surely or fails in eventually almost surely.

In this paper we define the strong convergence law for formulas, which carries over the ideas of the strong 0-1 law to formulas with free variables, and roughly states that for each formula ϕ(x), the fraction of tuples a in , which satisfy the formula ϕ(x), almost surely has a limit as n tends to infinity.

We show that the infinitary logic with finitely many variables has the strong convergence law for formulas for the uniform measure, and further characterize the measures on random graphs for which the strong convergence law holds.
The torsionfree part of the Ziegler spectrum of RG when R is a Dedekind domain and G is a finite group
Authors: Marcja A. , Prest M. , Toffalori C.
Published: December 2007

For every ring S with identity, the (right) Ziegler spectrum of S, Zgs, is the set of (isomorphism classes of) indecomposable pure injective (right) S-modules. The Ziegler topology equips Zgs with the structure of a topological space. A typical basic open set in this topology is of the form

where φ and ψ are pp-formulas (with at most one free variable) in the first order language Ls for S-modules; let [φ/ψ] denote the closed set Zgs - (φ/ψ). There is an alternative way to introduce the Ziegler topology on Zgs. For every choice of two f.p. (finitely presented) S-modules A, B and an S-module homomorphism f: A → B, consider the set (f) of the points N in Zgs such that some S-homomorphism h: A → N does not factor through f. Take (f) as a basic open set. The resulting topology on Zgs is, again, the Ziegler topology.

The algebraic and model-theoretic relevance of the Ziegler topology is discussed in [Z], [P] and in many subsequent papers, including [P1], [P2] and [P3], for instance. Here we are interested in the Ziegler spectrum ZgRG of a group ring RG, where R is a Dedekind domain of characteristic 0 (for example R could be the ring Z of integers) and G is a finite group. In particular we deal with the R-torsionfree points of ZgRG.

The main motivation for this is the study of RG-lattices (i.e., finitely generated R-torsionfree RG-modules).
On regular reduced products
Authors: Kennedy Juliette , Shelah Saharon
Published: December 2007

Assume (ℵ0, ℵ1) → (λ, λ+). Assume M is a model of a first order theory T of cardinality at most λ+ in a language of cardinality ≤ λ. Let N be a model with the same language. Let Δ be a set of first order formulas in and let D be a regular filter on λ. Then M is Δ-embeddable into the reduced power Nλ/D, provided that every Δ-existential formula true in M is true also in N. We obtain the following corollary: for M as above and D a regular ultrafilter over λ, Mλ/D is λ++-universal. Our second result is as follows: For i < μ let Mi, and Ni, be elementarily equivalent models of a language which has cardinality ≤ λ. Suppose D is a regular filter on λ and (ℵ0, ℵ1) → (λ, λ+) holds. We show that then the second player has a winning strategy in the Ehrenfeucht-Fraïssé game of length λ+ on ΠiMi/D and ΠiNi/D. This yields the following corollary: Assume GCH and λ regular (or just (ℵ0, ℵ1) → (λ, λ+) and 2λ = λ+. For L, Mi and Ni be as above, if D is a regular filter on λ, then ΠiMi/D ≅ ΠiNi/D.
On Lascar rank and Morley rank of definable groups in differentially closed fields
Authors: Pillay Anand , Pong Wai Yan
Published: December 2007

Morley rank and Lascar rank are equal on generic types of definable groups in differentially closed fields with finitely many commuting derivations.
Automorphism groups of models of Peano arithmetic
Authors: Schmerl James H.
Published: December 2007

Which groups are isomorphic to automorphism groups of models of Peano Arithmetic? It will be shown here that any group that has half a chance of being isomorphic to the automorphism group of some model of Peano Arithmetic actually is.

For any structure, let Aut() be its automorphism group. There are groups which are not isomorphic to any model= (N, +, ·, 0, 1, ≤) of PA. For example, it is clear that Aut(N), being a subgroup of Aut((, <)), must be torsion-free. However, as will be proved in this paper,if(A, <)is a linearly ordered set and G is a subgroup of Aut((A, <)),then there are modelsofPAsuch that Aut() ≅G.

Ifis a structure, then its automorphism group can be considered as a topological group by letting the stabilizers of finite subsets ofAbe the basic open subgroups. If′ is an expansion of, then Aut(′) is a closed subgroup of Aut(). Conversely, for any closed subgroupG≤ Aut() there is an expansion′ ofsuch that Aut(′) =G. Thus, ifis a model of PA, then Aut() is not only a subgroup of Aut((N, <)), but it is even aclosedsubgroup of Aut((N, ′)).

There is a characterization, due to Cohn [2] and to Conrad [3], of those groupsGwhich are isomorphic to closed subgroups of automorphism groups of linearly ordered sets.
IKP and friends
Authors: Lubarsky Robert S.
Published: December 2007

There has been increasing interest in intuitionistic methods over the years. Still, there has been relatively little work on intuitionistic set theory, and most of that has been on intuitionistic ZF. This investigation is about intuitionistic admissibility and theories of similar strength.

There are several more particular goals for this paper. One is just to get some more Kripke models of various set theories out there. Those papers that have dealt with IZF usually were more proof-theoretic in nature, and did not provide models. Furthermore, the inspirations for many of the constructions here are classical forcing arguments. Although the correspondence between the forcing and the Kripke constructions is not made tight, the relationship between these two methods is of interest (see [6] for instance) and some examples, even if only suggestive, should help us better understand the relationship between forcing and Kripke constructions. Along different lines, the subject of least and greatest fixed points of inductive definitions, while of interest to computer scientists, has yet to be studied constructively, and probably holds some surprises. Admissibility is of course the proper set-theoretic context for this study. Finally, while most of the classical material referred to here has long been standard, some of it has not been well codified and may even be unknown, so along the way we'll even fill in a gap in the classical literature.

The next section develops the basics of IKP, including some remarks on fixed points of inductive definitions.
Regular enumerations
Authors: Soskov I. N. , Baleva V.
Published: December 2007

In the paper we introduce and study regular enumerations for arbitrary recursive ordinals. Several applications of the technique are presented.
A uniqueness theorem for iterations
Authors: Larson Paul
Published: December 2007

If M is a countable transitive model of , then for every real x there is a unique shortest iteration j: M → N with x ∈ N, or none at all.
Cardinalities in the projective hierarchy
Authors: Hjorth Greg
Published: December 2007

We show that the “effective cardinality” of the collection of sets is strictly bigger than the effective cardinality of the . The phrase effective cardinality is vague but can be made exact in the usual ways. For instance:

Theorem 1.1. Assume ADL(ℝ)Then in L(ℝ) there is no injection

.

A few years ago Tony Martin showed a similar result, establishing the non-existence of an injection from to for m sufficiently larger than n. His method did not seem to work for m = n + 1.

This present paper gives level by level calculations for the projective hierarchy, but it too falls short of a complete analysis, in as much as it leaves the position of the effective cardinals in the Wadge degrees largely obscure. At the low levels it takes some time for any new cardinals to appear. Whenever Γ1, Γ2 are non-trivial Wadge degrees strictly included in one has

.
Splitting and nonsplitting, II: A low2 c.e. degree above which 0′ is not splittable
Authors: Cooper S. Barry , Li Angsheng
Published: December 2007

It is shown that there exists a low2 Harrington non-splitting base — that is, a low2 computably enumerable (c.e.) degree a such that for any c.e. degrees x, y, if 0′ = x ∨ y, then either 0′ = x ∨ a or 0′ = y ∨ a. Contrary to prior expectations, the standard Harrington non-splitting construction is incompatible with the low2-ness requirements to be satisfied, and the proof given involves new techniques with potentially wider application.
On iterating semiproper preorders
Authors: Miyamoto Tadatoshi
Published: December 2007

Let T be an ω1-Souslin tree. We show the property of forcing notions; “is {ω1}-semi-proper and preserves T” is preserved by a new kind of revised countable support iteration of arbitrary length. As an application we have a forcing axiom which is compatible with the existence of an ω1 -Souslin tree for preorders as wide as possible.
A rank for the class of elementary submodels of a superstable homogeneous model
Authors: Hyttinen Tapani , Lessmann Olivier
Published: December 2007

We study the class of elementary submodels of a large superstable homogeneous model. We introduce a rank which is bounded in the superstable case, and use it to define a dependence relation which shares many (but not all) of the properties of forking in the first order case. The main difference is that we do not have extension over all sets. We also present an example of Shelah showing that extension over all sets may not hold for any dependence relation for superstable homogeneous models.
A constructive look at the completeness of the space (ℝ)
Authors: Ishihara Hajime , Yoshida Satoru
Published: December 2007

We show, within the framework of Bishop's constructive mathematics, that (sequential) completeness of the locally convex space (ℝ) of test functions is equivalent to the principle BD-ℕ which holds in classical mathemtatics, Brouwer's intuitionism and Markov's constructive recursive mathematics, but does not hold in Bishop's constructivism.
Modulated fibring and the collapsing problem
Authors: Sernadas Cristina , Rasga João , Carnielli Walter A.
Published: December 2007

Fibring is recognized as one of the main mechanisms in combining logics, with great significance in the theory and applications of mathematical logic. However, an open challenge to fibring is posed by the collapsing problem: even when no symbols are shared, certain combinations of logics simply collapse to one of them, indicating that fibring imposes unwanted interconnections between the given logics. Modulated fibring allows a finer control of the combination, solving the collapsing problem both at the semantic and deductive levels. Main properties like soundness and completeness are shown to be preserved, comparison with fibring is discussed, and some important classes of examples are analyzed with respect to the collapsing problem.
Borovik-Poizat rank and stability
Authors: Burdges Jeffrey , Cherlin Gregory
Published: December 2007

Borovik proposed an axiomatic treatment of Morley rank in groups, later modified by Poizat, who showed that in the context of groups the resulting notion of rank provides a characterization of groups of finite Morley rank [2]. (This result makes use of ideas of Lascar, which it encapsulates in a neat way.) These axioms form the basis of the algebraic treatment of groups of finite Morley rank undertaken in [1].

There are, however, ranked structures, i.e., structures on which a Borovik-Poizat rank function is defined, which are not ℵ0-stable [1, p. 376]. In [2, p. 9] Poizat raised the issue of the relationship between this notion of rank and stability theory in the following terms: “… ungroupede Borovik est une structure stable, alors qu'un univers rangé n'a aucune raison de l'être …” (emphasis added). Nonetheless, we will prove the following:

Theorem 1.1.A ranked structure is superstable.

An example of a non-ℵ0-stable structure with Borovik-Poizat rank 2 is given in [1, p. 376]. Furthermore, it appears that this example can be modified in a straightforward way to give ℵ0-stable structures of Borovik-Poizat rank 2 in which the Morley rank is any countable ordinal (which would refute a claim of [1, p. 373, proof of C.4]). We have not checked the details. This does not leave much room for strenghthenings of our theorem. On the other hand, the proof of Theorem 1.1 does give a finite bound for the heights of certain trees of definable sets related to unsuperstability, as we will see in Section 5.
Contiguity and distributivity in the enumerable Turing degrees — Corrigendum
Authors: Downey Rodney G. , Lempp Steffen
Published: December 2007

A computably enumerable Turing degree a is called contiguous iff it contains only a single computably enumerable weak truth table degree (Ladner and Sasso [2]). In [1], the authors proved that a nonzero computably enumerable degree a is contiguous iff it is locally distributive, that is, for all a1, a2, c with a1 ∪a2 = a and c ≤ a, there exist ci, ≤ ai with c1 ∪ c2 = c.

To do this we supposed that W was a computably enumerable set and ∪ a computably set with a Turing functional Φ such that ΦW = U. Then we constructed computably enumerable sets A0, A1 and B together with functionals Γ0, Γ1, Γ, and Δ so that

and so as to satisfy all the requirements below.

That is, we built a degree-theoretical splitting A0, A1 of W and a set B ≤TW such that if we cannot beat all possible degree-theoretical splittings V0, V1 of B then we were able to witness the fact that U ≤WW (via Λ).

After the proof it was observed that the set U of the proof (page 1222, paragraph 4) needed only to be Δ20. It was then claimed that a consequence to the proof was that every contiguous computably enumerable degree was, in fact, strongly contiguous, in the sense that all (not necessarily computably enumerable) sets of the degree had the same weak truth table degree.
Group configurations and germs in simple theories
Authors: Ben-Yaacov Itay
Published: December 2007

We develop the theory of germs of generic functions in simple theories. Starting with an algebraic quadrangle (or other similar hypotheses), we obtain an “almost” generic group chunk, where the product is defined up to a bounded number of possible values. This is the first step towards the proof of the group configuration theorem for simple theories, which is completed in [3].
Finitude simple et structures o-minimales (Finiteness property implies o-minimality)
Authors: Lion Jean-Marie
Published: December 2007

L'objet de ce texte est de montrer que des fonctions qui appartiennent à une famille vérifiant une propriété de finitude a priori non uniforme sont en fait définissables dans une structure o-minimale.
Video Podcasting in Perspective: The History, Technology, Aesthetics, and Instructional Uses of a New Medium
Authors: Brown Abbie , Green Timothy D.
Published: December 2007

An examination of the current state of the art of podcasting, with a focus on video podcasting. Included are a review of the history and technical aspects of podcasting and an overview of current educational applications of podcasting. A detailed description of an experiment conducted in creating and distributing video podcast episodes is provided. Issues related to the development and distribution of podcasts are discussed.
A Web-Based Interactive Mapping System of State Wide School Performance: Integrating Google Maps Api Technology into Educational Achievement Data
Authors: Wang Kening , Mulvenon Sean W. , Stegman Charles , Anderson Travis
Published: December 2007

Google Maps API (Application Programming Interface), released in late June 2005 by Google, is an amazing technology that allows users to embed Google Maps in their own Web pages with JavaScript. Google Maps API has accelerated the development of new Google Maps based applications. This article reports a Web-based interactive mapping system building with Google Maps API, to map all Arkansas public schools and linking the school on the Google map with its longitudinal educational achievement database. The goal of this system is to disseminate the longitudinal statistical summaries of school performance produced by experts with the school geographical information to public users. Educators can use this interactive mapping system for local educational research, and for analyses of school improvement through accessing the longitudinal educational achievement data. Parents can use this system to get information for deciding which school would provide the best educational environment, so that they can choose the best and nearest school for their children.
The Impact of the Affinity Learning Authoring Tool on Student Learning
Authors: Soh Leen-Kiat , Fowler David , Zygielbaum Art I.
Published: December 2007

Affinity Learning is a system that allows the user to build a lesson on a subject matter by breaking it down into concepts, misconceptions, assessments, and remediation steps. Examples and questions can also used in these components. Affinity Learning has been found to be effective and can offer critical insights to student learning strategies. Authoring Affinity Learning lesson plans or hierarchies, however, is non-trivial. We have developed two authoring tools: the first tool provides an overall view of the hierarchy with a graphical display of the nodes and links; but the second tool does not. This article reports on a study conducted to test whether the graphical authoring tool can help produce better-quality hierarchies and also help the users learn about the subject matter better than the non-graphical authoring tool. Results show that while the graphical authoring tool can result in better-quality hierarchies, it does not result in better learning.
A Survey of Hardware and Software Technologies for the Rapid Development of Multimedia Instructional Modules
Authors: Ganesan Nanda
Published: December 2007

A survey of hardware and software technologies was conducted to identify suitable technologies for the development of instructional modules representing various instructional approaches. The approaches modeled were short PowerPoint presentations, chalk-and-talk type of lectures and software tutorials. The survey focused on identifying application development technologies that would help simulate the in-class learning experience in the modules. The scope of the survey was limited to those technologies that would facilitate the rapid development of multimedia modules by being simple to learn, use, and adopt. This article describes the survey in three fronts. First, the hardware components that are critical to the production of the multimedia modules are discussed. Second, different input devices are reviewed with a view of selecting a suitable device for simulating the chalk-and-talk type of lectures. Third, the authoring software currently available for producing software tutorials is discussed. The survey indicated that there are now powerful and affordable hardware and software that could be used effectively for the rapid development of multimedia modules. As a result, the use of instructional multimedia in classrooms is anticipated to grow as instructors become familiar with the emerging and maturing tools for instructional multimedia development.
Impact of Multi-Media Case Studies on Improving Intrinsic Learning Motivation of Students
Authors: Mehta Anju , Clayton Howard , Sankar Chetan S.
Published: December 2007

Past research has suggested that students need to be motivated by themselves (intrinsic learning motivation) and use higher-order cognitive skills so as to excel in problem solving, decision-making, and analytical reasoning in real-life situations. In this study, we examined the role of intrinsic learning motivation (ILM) and cumulative GPA in predicting perceived improvement of higher-order cognitive skills (HOCS). Business and engineering students attending three large universities were given an opportunity to analyze a multi-media case study that brings real-world issues into the classroom. Data on intrinsic learning motivation, cumulative GPA, and perceived improvement in Higher-order Cognitive Skills were collected. Structural Equation Modeling was then used to analyze the relationships. Results revealed that intrinsic learning motivation was significant and GPA insignificant in predicting perceived improvement of HOCS. Several implications emerge for business education and practice. For example, the findings provide suggestions for introducing innovative instructional tools to enhance students' cognitive skills. For practitioners, the results indicate the need to use tests of intrinsic learning motivation for jobs requiring HOCS.
Luminescence Dating of the Morasko (Poland), Kaali, Ilumetsa and Tsõõrikmäe (Estonia) Meteorite Craters
Authors: Stankowski Wojciech , Raukas Anto , Bluszcz Andrzej , Fedorowicz Stanisław
Published: December 2007

The TL dating of sinter crust of Morasko meteorites proves that the extraterrestrial matter fell about 5000 yr BP. Similar data were obtained for the Kaali impact. The OSL analyses show incomplete bleaching of old rock material especially in the Estonian craters. Almost all data obtained for the immediate impact area indicate ages younger than the Quaternary morphogenesis. The method used seems promising for determining the age of impacts and the origin of small depressions of unknown genesis.
Interaction Between Certain Moulds and Aflatoxin B1 Producer Aspergillus Flavus NRRL 3251
Authors: Cvetnić Zdenka , Pepeljnjak Stjepan
Published: December 2007

Interaction Between Certain Moulds and Aflatoxin B1ProducerAspergillus FlavusNRRL 3251

The objective of this study was to evaluate biotic interaction between some mould species and active producer of aflatoxin B1Aspergillus flavusNRRL 3251, co-cultured in yeast-extract sucrose (YES) broth. Twenty-five mould strains ofAlternariaspp.,Cladosporiumspp.,Mucorspp.,A. flavusandA. niger, used as biocompetitive agents, were isolated from outdoor and indoor airborne fungi, scrapings of mouldy household walls, and from stored and post-harvest maize. Aflatoxin B1was extracted from mould biomasses with chloroform and detected using the multitoxin TLC method. The results confirm antagonistic interaction between all strains tested. WithAlternariaspp. andCladosporiumspp., aflatoxin B1production decreased 100 %, compared to detection in a single culture ofA. flavusNRRL 3251 (Cmean=18.7 μg mL-1). In mixed cultures withMucorspp., aflatoxinB1levels dropped to (5.6-9.3) μg mL-1, and the inhibition was from 50 % to 70 %. Four of five aflatoxin non-producing strains ofA. flavusinterfered with aflatoxin production in mixed culture, and reduced AFB1productivity by 100 %. One strain showed a lower efficacy in inhibiting AFB1production (80 %) with a detectable amount of AFB13.7 μg mL-1when compared to control. A decrease in toxin production was also observed in dual cultivation withA. nigerstrains. It resulted in 100 % reduction in three strains), 90 % reduction in one strain (Cmean=1.9 μg mL-1) and 80 % reduction in one strain (Cmean=3.7 μg mL-1) inhibition.
Endocrinological and Behavioural Effects of Chronic Fluxilan Administration in Rats
Authors: Spasojević Nataša , Gavrilović Ljubica , Kovačević Ivan , Dronjak Slađana
Published: December 2007

Endocrinological and Behavioural Effects of Chronic Fluxilan Administration in Rats

Chronic stress induces changes in the neuroendocrine and neuronal system, including elevation of catecholamines and corticosterone (CORT) levels, and could be an important factor in initial depression. Antidepressants affect monoaminergic neurotransmission and modulate central neuropeptides involved in the coordination of stress response and the control of HPA axis activity. We studied the effects of chronic treatment with fluxilan, a selective inhibitor of serotonin reuptake, in unstressed controls and chronic unpredictable mild stress (CUMS) rats, on behaviour and plasma noradrenaline (NA), adrenaline (A), corticosterone (CORT) and adrenocorticotropic hormone (ACTH). CUMS did not affect plasma NA, A and ACTH, but elevated plasma CORT content. Plasma concentration of catecholamines after fluxilan administration was significantly increased in control and CUMS group. On the other hand, fluxilan expressed no effect on plasma ACTH and CORT concentrations in control animals, but decreased ACTH and CORT levels in CUMS animals. Behaviourally, fluxilan treated animals displayed enhanced anxiety. The results demonstrate that the anxiogenic effects of chronic fluxilan administration are similar to those reported by many other studies. The findings described here suggest that elevated plasma catecholamines may contribute to an adverse effect of this drug on cardiovascular parameters during antidepressant therapy.
The Diagnostic Value of Anti-Cyclic Citrullinated Peptide Antibodies (anti-CCP) in Patients with Rheumatoid Arthritis
Authors: Damjanovska Ljubinka , Atanasovska Violeta , Gruev Todor
Published: December 2007

The Diagnostic Value of Anti-Cyclic Citrullinated Peptide Antibodies (anti-CCP) in Patients with Rheumatoid Arthritis

A cross-sectional study was carried out to analyze the prevalence of anti-CCP antibodies and IgM RF in the sera of 160 randomly selected patients from the Rheumatology Department: 60 with RA, 50 with other rheumatic diseases (non-RA), 50 healthy controls (HC). The mean age of the group was 50.06+/-11.9 years. There were 141 females (88.1%) and 19 males (11.9%). RA patients fulfilled the revised ACR criteria. The mean duration of the disease was 82.4 months. Anti-CCP ELISA kit and IgM RF Latex test were used. The mean anti-CCP values were as follows: RA 60.4+/-57.6, non-RA 2.1+/-3.6, HC 1.3 +/-0.4 U/mL. Respectively, the mean values of IgM RF were: RA 515.8+/-525, non-RA 102+/-294, HC 15+/-57.5. Forty out of 60 (66.6%) RA patients were anti-CCP positive. Forty one out of 60 (68.3%) RA patients were positive for IgM RF. As expected, anti-CCP showed comparable sensitivity (66.8% vs. 68.3%) and higher specificity (98% vs. 87%) than IgM RF, at optimal cut-off values. The presence of either anti-CCP or IgM RF increased the testing sensitivity for the diagnosis of RA to 76.6%. AUC was greater for anti-CCP than for IgM RF (0.92 vs. 0.82).
Aminoglycosides and Kidney Function
Authors: Stanić Momčilo , Mitić Radoslav , Jakovljević Milan
Published: December 2007

Aminoglycosides and Kidney Function

The aminoglycosides are bactericide antibiotics with predominant effecting on the Gramm-negative bacteries, then staphylococci and mycobacteria with a small therapeutic range and with expressive ototoxic, nephrotoxic and with rare neurotoxic side effects. In this work the value of creatinine are investigated in serum of patients who are hospitalized in Internal department of the Health Center in Kosovska Mitrovica, before, in the course of and after therapy with the aminoglycosides antibiotics were given in different doses. The creatinine was determined by kinetic method (Jaffe). The significant increasing of creatinine values in serum was recorded with the groups of patients who have got gentamicine 2x120 mg i.m., gentamicine 2x120 mg in combination with furosemide, the gentamicine 2x120 mg with the patients with diabetes mellitus, gentamicine 2x120 mg in the course of 14 days until with the groups who have been getting gentamicine 1x120 mg, gentamicine 2x80 mg and amikacine 2x500 mg were not recorded the significant increased values of creatinine. The determination of creatinine for the sake of the following degree damage of kidney function in the course therapy of the aminoglycosides was very important.
The Proposal for Solution of Interference Problems Caused By Drugs
Authors: Jovanović Slobodan , Birinji Klara
Published: December 2007

The Proposal for Solution of Interference Problems Caused By Drugs

For long years the laboratories have the problem of endogenous and axogenous interferences. Drugs are responsable for more than 90% of exogenous interference. The aim of the investigation was to find a rather simple and economic way in solution of every day existing problem in clinical biochemistry. Using the appropriate literature the possible existing of interference is determined. Such approach could be interesting for many of laboratories in every day practice.
Gamma Knife surgery and trigeminal schwannoma: is it possible to preserve cranial nerve function?
Authors: Phi Ji Hoon , Paek Sun Ha , Chung Hyun-Tai , Jeong Sang Soon , Park Chul-Kee , Jung Hee-Won , Kim Dong Gyu
Published: December 2007

Object

The current study was undertaken to evaluate the tumor control rate and functional outcome after Gamma Knife surgery (GKS) in patients with a trigeminal schwannoma. The conditions associated with the development of cranial neuropathies after radiosurgery were scrutinized.

Methods

The authors reviewed the clinical records and radiological data in 22 consecutive patients who received GKS for a trigeminal schwannoma. The median tumor volume was 4.1 ml (0.2–12.0 ml), and the mean tumor margin dose was 13.3 ± 1.3 Gy at an isodose line of 49.9 ± 0.6% (mean ± standard deviation). The median clinical follow-up period was 46 months (range 24–89 months), and the median length of imaging follow-up was 37 months (range 24–79 months).

Results

Tumor growth control was achieved in 21 (95%) of the 22 patients. Facial pain responded best to radio-surgery, with two thirds of patients showing improvement. However, only one third of patients with facial hypesthesia improved. Six patients (27%) experienced new or worsening cranial neuropathies after GKS. Ten patients (46%) showed tumor expansion after radiosurgery, and nine of these also showed central enhancement loss. Loss of central enhancement, tumor expansion, and a tumor in a cavernous sinus were found to be significantly related to the emergence of cranial neuropathies.

Conclusions

The use of GKS to treat trigeminal schwannoma resulted in a high rate of tumor control and functional improvement. Cranial neuropathies are bothersome complications of radiosurgery, and tumor expansion in a cavernous sinus after radiosurgery appears to be the proximate cause of the complication. Loss of central enhancement could be used as a warning sign of cranial neuropathies, and for this vigilant patient monitoring is required.
Is repeated radiosurgery an alternative to staged radiosurgery for very large brain arteriovenous malformations?
Authors: Karlsson Bengt , Jokura Hidefumi , Yamamoto Masaaki , Söderman Michael , Lax Ingmar
Published: December 2007

Object

The results of a novel radiosurgical approach to treat large arteriovenous malformations (AVMs) with repeated radiosurgery are presented and discussed.

Methods

The outcome was studied following repeated Gamma Knife surgery (GKS) for large AVMs, defined as a nidus volume of 9 ml or more. The philosophy was to treat the whole AVM with a low dose of radiation (≥ 10 Gy), and to repeat the treatment if the AVM shrank but was not obliterated. The study included 133 patients with AVMs treated at one of three different institutions. Clinical information was available for all patients, and complete radiological follow-up was available in 89 patients after the first treatment, and in 19 after the second treatment.

Results

The estimated obliteration rate following repeated GKS was 62%. Four patients (3%) developed neurological deficits caused by the radiation, whereas five others (4%) developed cystic changes. The annual incidence of hemorrhage was high (7%), of which 35% occurred within the 1st year after the first treatment.

Conclusions

Repeated radiosurgery seems to be a viable option for some AVMs considered to be too large for conventional radiosurgical treatment. The incidence of posttreatment hemorrhages seems to be a larger clinical problem than radiation-induced complications.