bluuebunny/crossref_metadata_2025_split huggingface dataset:
Contribution of Direct Heating, Thermal Conduction and Perfusion During Radiofrequency and Microwave Ablation
Authors: Schramm Wolfgang , Yang Deshan , Wood Bradford J , Rattay Frank , Haemmerich Dieter 
Published: December 2007

Both radiofrequency (RF) and microwave (MW) ablation devices are clinically used for tumor ablation. Several studies report less dependence on vascular mediated cooling of MW compared to RF ablation. We created computer models of a cooled RF needle electrode, and a dipole MW antenna to determine differences in tissue heat transfer.
We created Finite Element computer models of a RF electrode (Cooled needle, 17 gauge), and a MW antenna (Dipole, 13 gauge). We simulated RF ablation for 12 min with power controlled to keep maximum tissue temperature at 100 ºC, and MW ablation for 6 min with 75 W of power applied. For both models we considered change in electric and thermal tissue properties as well as perfusion depending on tissue temperature. We determined tissue temperature profile at the end of the ablation procedure and calculated effect of perfusion on both RF and MW ablation.
Maximum tissue temperature was 100 ºC for RF ablation, and 177 ºC for MW ablation. Lesion shape was ellipsoid for RF, and tear-drop shaped for MW ablation. MW ablation is less affected by tissue perfusion mainly due to the shorter ablation time and higher tissue temperature, but not due to MW providing deeper heating than RF. Both MW and RF applicators only produce significant direct heating within mm of the applicator, with most of the ablation zone created by thermal conduction.
Both RF and MW applicators only directly heat tissue in close proximity of the applicators. MW ablation allows for higher tissue temperatures than RF since MW propagation is not limited by tissue desiccation and charring. Higher temperatures coupled with lower treatment times result in reduced effects of perfusion on MW ablation.
The geometry of non-distributive logics
Authors: Restall Greg , Paoli Francesco 
Published: December 2007

AbstractIn this paper we introduce a new natural deduction system for the logic of lattices, and a number of extensions of lattice logic with different negation connectives. We provide the class of natural deduction proofs with both a standard inductive definition and a global graph-theoretical criterion for correctness, and we show how normalisation in this system corresponds to cut elimination in the sequent calculus for lattice logic. This natural deduction system is inspired both by Shoesmith and Smiley's multiple conclusion systems for classical logic and Girard's proofnets for linear logic.
Logical consecutions in discrete linear temporal logic
Authors: Rybakov V. V. 
Published: December 2007

AbstractWe investigate logical consequence in temporal logics in terms of logical consecutions, i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be ‘correct’ in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logicLDTL, consisting of all formulas valid in the frame 〈L≤, ≥〉 of all integer numbers, is the prime object of our investigation. We describe consecutions admissible inLDTLin a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible inLDTL. Also, we note that using the same technique it follows that the linear temporal logicL(N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logicsLDTLandL(N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (known fact), and the given deciding algorithms are explicit.
PFA implies ADL(ℝ)
Authors: Steel John R. 
Published: December 2007

In this paper we shall proveTheorem 0.1. Suppose there is a singular strong limit cardinal κ such that □κ fails; then AD holds in L(R).See [10] for a discussion of the background to this problem. We suspect that more work will produce a proof of the theorem with its hypothesis that κ is a strong limit weakened to ∀α < κ (αω < κ), and significantly more work will enable one to drop the hypothesis that K is a strong limit entirely. At present, we do not see how to carry out even the less ambitious project.Todorcevic [23] has shown that if the Proper Forcing Axiom (PFA) holds, then □κ fails for all uncountable cardinals κ. Thus we get immediately:It has been known since the early 90's that PFA implies PD, that PFA plus the existence of a strongly inaccessible cardinal implies ADL(ℝ) and that PFA plus a measurable yields an inner model of ADℝ containing all reals and ordinals. As we do here, these arguments made use of Tororcevic's work, so that logical strength is ultimately coming from a failure of covering for some appropriate core models.In late 2000, A. S. Zoble and the author showed that (certain consequences of) Todorcevic's Strong Reflection Principle (SRP) imply ADL(ℝ). (See [22].) Since Martin's Maximum implies SRP, this gave the first derivation of ADL(ℝ) from an “unaugmented” forcing axiom.
Properties and consequences of Thorn-independence
Authors: Onshuus Alf 
Published: December 2007

AbstractWe develop a new notion of independence (ϸ-independence, read “thorn”-independence) that arises from a family of ranks suggested by Scanlon (ϸ-ranks). We prove that in a large class of theories (including simple theories and o-minimal theories) this notion has many of the properties needed for an adequate geometric structure.We prove that ϸ-independence agrees with the usual independence notions in stable, supersimple and o-minimal theories. Furthermore, we give some evidence that the equivalence between forking and ϸ-forking in simple theories might be closely related to one of the main open conjectures in simplicity theory, the stable forking conjecture. In particular, we prove that in any simple theory where the stable forking conjecture holds, ϸ-independence and forking independence agree.
Automorphism groups of arithmetically saturated models
Authors: Nurkhaidarov Ermek S. 
Published: December 2007

In this paper we study the automorphism groups of countable arithmetically saturated models of Peano Arithmetic. The automorphism groups of such structures form a rich class of permutation groups. When studying the automorphism group of a model, one is interested to what extent a model is recoverable from its automorphism group. Kossak-Schmerl [12] show that ifMis a countable, arithmetically saturated model of Peano Arithmetic, then Aut(M) codes SSy(M). Using that result they prove:Let M1. M2be countable arithmetically saturated models of Peano Arithmetic such that Aut(M1)≅ Aut(M2).ThenSSy(M1) = SSy(M2).We show that ifMis a countable arithmetically saturated of Peano Arithmetic, then Aut(M) can recognize if some maximal open subgroup is a stabilizer of a nonstandard element, which is smaller than any nonstandard definable element. That fact is used to show the main theorem:Let M1,M2be countable arithmetically saturated models of Peano Arithmetic such thatAut(M1) ≅ Aut(M2).Then for every n<ωHere RT2nis Infinite Ramsey's Theorem stating that every 2-coloring of [ω]nhas an infinite homogeneous set. Theorem 0.2 shows that for models of a false arithmetic the converse of Kossak-Schmerl Theorem 0.1 is not true. Using the results of Reverse Mathematics we obtain the following corollary:There exist four countable arithmetically saturated models of Peano Arithmetic such that they have the same standard system but their automorphism groups are pairwise non-isomorphic.
Permutations and wellfoundedness: the true meaning of the bizarre arithmetic of Quine's NF
Authors: Forster Thomas 
Published: December 2007

AbstractIt is shown that, according to NF, many of the assertions of ordinal arithmetic involving theT-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-permutation-models of assertions which have perfectly sensible ZF-style meanings, such as: the existence of wellfounded sets of great size or rank, or the nonexistence of small counterexamples to the wellfoundedness of ∈. Everything here holds also for NFU if the permutations are taken to fix allurelemente.
Completeness and Herbrand theorems for nominal logic
Authors: Cheney James 
Published: December 2007

AbstractNominal logic is a variant of first-order logic in which abstract syntax with names and binding is formalized in terms of two basic operations:name-swapping andfreshness. It relies on two important principles:equivariance(validity is preserved by name-swapping), andfresh name generation(“new” or fresh names can always be chosen). It is inspired by a particular class of models for abstract syntax trees involving names and binding, drawing on ideas from Fraenkel-Mostowski set theory:finite-support modelsin which each value can depend on only finitely many names.Although nominal logic is sound with respect to such models, it is not complete. In this paper we review nominal logic and show why finite-support models are insufficient both in theory and practice. We then identify (up to isomorphism) the class of models with respect to which nominal logic is complete:ideal-supportedmodels in which the supports of values are elements of a proper ideal on the set of names.We also investigate an appropriate generalization of Herbrand models to nominal logic. After adjusting the syntax of nominal logic to include constants denoting names, we generalizeuniversaltheories tonominal-universaltheories and prove that each such theory has an Herbrand model.
Morley degree in unidimensional compact complex spaces
Authors: Radin Dale 
Published: December 2007

AbstractLetbe the category of all reduced compact complex spaces, viewed as a multi-sorted first order structure, in the standard way. Letbe a sub-category of. which is closed under the taking of products and analytic subsets, and whose morphisms include the projections. Under the assumption that Th() is unidimensional. we show that Morley rank is equal to Noetherian dimension, in any elementary extension of. As a result, we are able to show that Morley degree is definable in Th(). when Th() is unidimensional.
On theories and models in fuzzy predicate logics
Authors: Hájek Petr , Cintula Petr 
Published: December 2007

AbstractIn the last few decades many formal systems of fuzzy logics have been developed. Since the main differences between fuzzy and classical logics lie at the propositional level, the fuzzy predicate logics have developed more slowly (compared to the propositional ones). In this text we aim to promote interest in fuzzy predicate logics by contributing to the model theory of fuzzy predicate logics. First, we generalize the completeness theorem, then we use it to get results on conservative extensions of theories and on witnessed models.
Truth In V for ∃*∀∀-Sentences is Decidable
Authors: Bellé D. , Parlamento F. 
Published: December 2007

AbstractLet V be the cumulative set theoretic hierarchy, generated from the empty set by taking powers at successor stages and unions at limit stages and. following [2], let the primitive language of set theory be the first order language which contains binary symbols for equality and membership only. Despite the existence of ∀∀-formulae in the primitive language, with two free variables, which are satisfiable in ∀ but not by finite sets ([5]). and therefore of ∃∃∀∀ sentences of the same language, which are undecidable in ZFC without the Axiom of Infinity, truth in V for ∃*∀∀-sentences of the primitive language, is decidable ([1]). Completeness of ZF with respect to such sentences follows.
The Π3-theory of the -enumeration degrees is undecidable
Authors: Kent Thomas F. 
Published: December 2007

AbstractWe show that in the language of { ≤ }. the Π3-fragment of the first order theory of the -enumeration degrees is undecidable. We then extend this result to show that the Π3-theory of any substructure of the enumeration degrees which contains the -degrees is undecidable.
Bounds for covering numbers
Authors: Liu Andreas 
Published: December 2007

AbstractLetλbe a singular cardinal of uncountable cofinalityν. Under various assumptions about the sizes of covering families for cardinals belowλ, we prove upper bounds for the covering number COV(λ. λ. ν+. 2). This covering number is closely related to the cofinality of the partial order ([λ]ν. ⊆).
Theories very close to PA where Kreisel's Conjecture is false
Authors: Hrubeš Pavel 
Published: December 2007

AbstractWe give four examples of theories in which Kreisel's Conjecture is false: (1) the theory PA(-) obtained by adding a function symbol minus, ‘—’, to the language of PA, and the axiom ∀x∀y∀z (x − y = z) ≡ (x = y + z ∨ (x < y ∧ z = 0)); (2) the theory L of integers; (3) the theory PA(q) obtained by adding a function symbol q (of arity ≥ 1) to PA, assuming nothing about q; (4) the theory PA(N) containing a unary predicate N(x) meaning ‘x is a natural number’. In Section 6 we suggest a counterexample to the so called Sharpened Kreisel's Conjecture.
The nonstationary ideal in the ℙmax extension
Authors: Larson Paul B. 
Published: December 2007

AbstractThe forcing construction ℙmax, invented by W. Hugh Woodin, produces a model whose collection of subsets of ω1 is in some sense maximal. In this paper we study the Boolean algebra induced by the nonstationary ideal on ω1 in this model. Among other things we show that the induced quotient does not have a simply definable form. We also prove several results about saturation properties of the ideal in this extension.
Elementary differences between the (2p)-C. E. and the (2p +1)-c. e. enumeration degrees
Authors: Kalimullin I. S. 
Published: December 2007

AbstractIt is proved that the (2p)-c. e. e-degrees are not elementarily equivalent to the (2p + 1)-c. e. e-degrees for each nonzero p ∈ ω. It follows that m-c. e. e-degrees are not elementarily equivalent to the n-c e. e-degrees if 1 <m < n.
A Reduction of the NF consistency Problem
Authors: Tzouvaras Athanassios 
Published: December 2007

AbstractWe give a necessary and sufficient condition in order that a type-shifting automorphism be constructed on a model of the Theory of Simple Types (TST) by forcing. Namely it is proved that, if for every n ≥ 1 there is a model of TST in the ground model M of ZFC that contains an n-extendible coherent pair, then there is a generic extension M[G] of M that contains a model of TST with a type-shifting automorphism, and hence M[G] contains a model of NF. The converse holds trivially. It is also proved that there exist models of TST containing 1-extendible coherent pairs.
Spectra of structures and relations
Authors: Harizanov Valentina S. , Miller Russell G. 
Published: December 2007

AbstractWe consider embeddings of structures which preserve spectra: if g : ℳ → with computable, then ℳ should have the same Turing degree spectrum (as a structure) that g(ℳ) has (as a relation on ). We show that the computable dense linear order ℒ is universal for all countable linear orders under this notion of embedding, and we establish a similar result for the computable random graph Such structures are said to be spectrally universal. We use our results to answer a question of Goncharov, and also to characterize the possible spectra of structures as precisely the spectra of unary relations on . Finally, we consider the extent to which all spectra of unary relations on the structure ℒ may be realized by such embeddings, offering partial results and building the first known example of a structure whose spectrum contains precisely those degrees c with c′ ≥ τ 0″.
Forcing indestructibility of set-theoretic axioms
Authors: KÖnig Bernhard 
Published: December 2007

AbstractVarious theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Lévy collapse. These show in particular that certain applications of forcing axioms require to add generic countable sequences high up in the set-theoretic hierarchy even before collapsing everything down to ℵ1. Later we give applications, among them the consistency of MM with ℵω not being Jónsson which answers a question raised in the set theory meeting at Oberwolfach in 2005.
Ideal convergence of bounded sequences
Authors: Filipów Rafał , Mrożek Nikodem , Recław Ireneusz , Szuca Piotr 
Published: December 2007

AbstractWe generalize the Bolzano-Weierstrass theorem (that every bounded sequence of reals admits a convergent subsequence) on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals and quotient Boolean algebras. In particular we show that an ideal does not have BW property if and only if its quotient Boolean algebra has a countably splitting family.
An analysis of the W*-hierarchy
Authors: Chen Yijia , Flum Jörg , Grohe Martin 
Published: December 2007

AbstractWe observe that the W*-hierarchy, a variant (introduced by Downey, Fellows, and Taylor [7]) of the better known W-hierarchy, coincides with the W-hierarchy, though not level wise, but just as a whole hierarchy. More precisely, we prove that W[t] ⊆ W* [t] ⊆ W[2t − 2] for each t ≥ 2. It was known before that W[1] = W*[1] and W[2] = W*[2].Our second main result is a new logical characterization of the W*-hierarchy in terms of “Fagin-definable problems.” As a by-product, we also obtain an improvement of our earlier characterization of the hierarchy in terms of model-checking problems. Furthermore, we obtain new complete problems for the classes W[3] and W*[3].
Connecting many-sorted theories
Authors: Baader Franz , Ghilardi Silvio 
Published: December 2007

AbstractBasically, the connection of two many-sorted theories is obtained by taking their disjoint union, and then connecting the two parts through connection functions that must behave like homomorphisms on the shared signature. We determine conditions under which decidability of the validity of universal formulae in the component theories transfers to their connection. In addition, we consider variants of the basic connection scheme. Our results can be seen as a generalization of the so-called -connection approach for combining modal logics to an algebraic setting.
Transfer principle in quantum set theory
Authors: Ozawa Masanao 
Published: December 2007

AbstractIn 1981, Takeuti introduced quantum set theory as the quantum counterpart of Boolean valued models of set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed subspaces in a Hilbert space and showed that appropriate quantum counterparts of ZFC axioms hold in the model. Here, Takeuti's formulation is extended to construct a model of set theory based on the logic represented by the lattice of projections in an arbitrary von Neumann algebra. A transfer principle is established that enables us to transfer theorems of ZFC to their quantum counterparts holding in the model. The set of real numbers in the model is shown to be in one-to-one correspondence with the set of self-adjoint operators affiliated with the von Neumann algebra generated by the logic. Despite the difficulty pointed out by Takeuti that equality axioms do not generally hold in quantum set theory, it is shown that equality axioms hold for any real numbers in the model. It is also shown that any observational proposition in quantum mechanics can be represented by a corresponding statement for real numbers in the model with the truth value consistent with the standard formulation of quantum mechanics, and that the equality relation between two real numbers in the model is equivalent with the notion of perfect correlation between corresponding observables (self-adjoint operators) in quantum mechanics. The paper is concluded with some remarks on the relevance to quantum set theory of the choice of the implication connective in quantum logic.
Assignment of ordinals to patterns of resemblance
Authors: Wilken Gunnar 
Published: December 2007

AbstractIn [2] T. J. Carlson introduces an approach to ordinal notation systems which is based on the notion of Σ1-elementary substructure. We gave a detailed ordinal arithmetical analysis (see [7]) of the ordinal structure based on Σ1-elementarily as defined in [2]. This involved the development of an appropriate ordinal arithmetic that is based on a system of classical ordinal notations derived from Skolem hull operators, see [6]. In the present paper we establish an effective order isomorphism between the classical and the new system of ordinal notations using the results from [6] and [7]. Moreover, on the basis of a concept of relativization we develop mutual (relatively) elementary recursive assignments which are uniform with respect to the underlying relativization.
Local Kc constructions
Authors: Steel J. R. 
Published: December 2007

The full-background-extender Kc -construction of [2] has the property that, if it does not break down and produces a final model , thenΉ is Woodin in V ⇒ Ή is Woodin in ,for all Ή. It is natural to ask whetherκ is strong in V ⇒ κ is λ-strong in ,for all κ, or even better,κ is λ-strong in V ⇒ κ is λ-strong in .As one might suspect, the more useful answer would be “yes”.For the Kc-construction of [2], this question is open. The problem is that the construction of [2] is not local: because of the full-background-extender demand, it may produce mice projecting to ρ at stages much greater than ρ. Because of this, there is no reason to believe that if E is a λ-strong extender of V, then The natural proof only gives that if κ is Σ2-strong, then Σ, is strong in .We do not know how to get started on this question, and suspect that in fact strong cardinals in V may fail to be strong in , if is the output of the construction of [2]. Therefore, we shall look for a modification of the construction of [2]. One might ask for a construction with output such that(1) iteration trees on can be lifted to iteration trees on V,(2) ∀δ(δ is Woodin ⇒ δ is Woodin in ), and(3) (a) ↾κ(κ is a strong cardinal ⇒ κ is strong in ), and (b) ↾κ↾λ(Lim(λ) Λ κ is λ-strong ⇒ κ is λ-strong in ).
An algebraic characterization of equivalent preferential models
Authors: Zhu Zhaohui , Zhang Rong 
Published: December 2007

AbstractPreferential models is one of the important semantical structures in nonmonotonic logic. This paper aims to establish an isomorphism theorem for preferential models, which gives us a purely algebraic characterization of the equivalence of preferential models. To this end, we present the notions of local similarity and local simulation. Based on these notions, two operators Δ(•) and μ(•) over preferential models are introduced and explored respectively. Together with other two existent operators ρ(•) and ΠD(•), we introduce an operator ∂D(•). Then the isomorphism theorem is obtained in terms of ∂D(•), which asserts that for any two preferential modelsM1andM2, they generate the same preferential inference if and only if ∂D(M1) and ∂D(M2) are isomorphic. Based on ∂D(•), we also get an alternative model-theoretical characterization of the well-known postulateWeaken Disjunctive Rationality. Moreover, in the finite language framework, we show that Δ(μ(•)) is competent for the task of eliminating redundancy, and provide a representation result fork-relations.