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1.
Roman Murawski 《Mathematical Logic Quarterly》1992,38(1):59-84
We consider iterations of satisfaction classes and apply them to construct expansions of models of Peano arithmetic to models of A|Δ+∑-AC. 1991 MSC: 03F35, 03C62. 相似文献
2.
Zoran Markovi&#x; 《Mathematical Logic Quarterly》1993,39(1):531-538
Since in Heyting Arithmetic (HA) all atomic formulas are decidable, a Kripke model for HA may be regarded classically as a collection of classical structures for the language of arithmetic, partially ordered by the submodel relation. The obvious question is then: are these classical structures models of Peano Arithmetic (PA)? And dually: if a collection of models of PA, partially ordered by the submodel relation, is regarded as a Kripke model, is it a model of HA? Some partial answers to these questions were obtained in [6], [3], [1] and [2]. Here we present some results in the same direction, announced in [7]. In particular, it is proved that the classical structures at the nodes of a Kripke model of HA must be models of IΔ1 (PA- with induction for provably Δ1 formulas) and that the relation between these classical structures must be that of a Δ1-elementary submodel. MSC: 03F30, 03F55. 相似文献
3.
Let M be a model of first order Peano arithmetic ( PA ) and I an initial segment of M that is closed under multiplication. LetM0 be the {0, 1,+}‐reduct ofM. We show that there is another model N of PA that is also an expansion of M0 such that a · M a = a · N a if and only if a ∈ I for all a ∈ M. 相似文献
4.
Arnold Beckmann Chris Pollett Samuel R. Buss 《Annals of Pure and Applied Logic》2003,120(1-3):197-223
This paper investigates provability and non-provability of well-foundedness of ordinal notations in weak theories of bounded arithmetic. We define a notion of well-foundedness on bounded domains. We show that T21 and S22 can prove the well-foundedness on bounded domains of the ordinal notations below 0 and Γ0. As a corollary, the class of polynomial local search problems, PLS, can be augmented with cost functions that take ordinal values below 0 and Γ0 without increasing the class PLS. 相似文献
5.
Dev K. Roy 《Mathematical Logic Quarterly》2003,49(1):83-86
The shortest definition of a number by a first order formula with one free variable, where the notion of a formula defining a number extends a notion used by Boolos in a proof of the Incompleteness Theorem, is shown to be non computable. This is followed by an examination of the complexity of sets associated with this function. 相似文献
6.
7.
Andreas Weiermann 《Mathematical Logic Quarterly》2007,53(1):4-18
We classify the phase transition thresholds from provability to unprovability for certain Friedman-style miniaturizations of Kruskal's Theorem and Higman's Lemma. In addition we prove a new and unexpected phase transition result for ε0. Motivated by renormalization and universality issues from statistical physics we finally state a universality hypothesis. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
Saharon Shelah 《Mathematical Logic Quarterly》2011,57(4):341-365
We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of ${mathbb N}$ such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of ${mathbb N}$ such that expanding ${mathbb N}$ by any uncountably many of them suffice. Also we find arithmetically closed ${mathcal A}$ with no ultrafilter on it with suitable definability demand (related to being Ramsey). © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
9.
Continuing the earlier research in [14] we give some more information about nonmaximal open subgroups of G = Aut(ℳ) with unique maximal extension, where ℳ is a countable recursively saturated model of True Arithmetic. 相似文献
10.
Jeremy Avigad 《Mathematical Logic Quarterly》2002,48(1):3-13
The 1‐consistency of arithmetic is shown to be equiva ent to the existence of fixed points of a certain type of update procedure, which is implicit in the epsilon‐substitution method. 相似文献
11.
Let be a nonstandard model of Peano Arithmetic with domain M and let be nonstandard. We study the symmetric and alternating groups S
n
and A
n
of permutations of the set internal to , and classify all their normal subgroups, identifying many externally defined such normal subgroups in the process. We provide
evidence that A
n
and S
n
are not split extensions by these normal subgroups, by showing that any such complement if it exists, cannot be a limit of
definable sets. We conclude by identifying an -valued metric on and (where B
S
, B
A
are the maximal normal subgroups of S
n
and A
n
identified earlier) making these groups into topological groups, and by showing that if is -saturated then and are complete with respect to this metric.
相似文献
12.
Teresa Bigorajska 《Mathematical Logic Quarterly》2003,49(1):101-108
Continuing the earlier research in [1] and [4] we work out a class of interstices in countable arithmetically saturated models of PA in which selective types are realized and a class of interstices in which 2‐indiscernible types are realized (and hence, there exist elements whose stabilizers are strongly maximal) 相似文献
13.
Grzegorz Michalski 《Mathematical Logic Quarterly》1995,41(4):515-522
We show that that every countable model of PA has a conservative extension M with a subset Y such that a certain Σ1(Y)-formula defines in M a subset which is not r. e. relative to Y. 相似文献
14.
We first note that Gentzen's proof-reduction for his consistency proof of PA can be directly interpreted as moves of Kirby-Paris' Hydra Game, which implies a direct independence proof of the game (Section 1 and Appendix). Buchholz's Hydra Game for labeled hydras is known to be much stronger than PA. However, we show that the one-dimensional version of Buchholz's Game can be exactly identified to Kirby-Paris' Game (which is two-dimensional but without labels), by a simple and natural interpretation (Section 2). Jervell proposed another type of a combinatorial game, by abstracting Gentzen's proof-reductions and showed that his game is independent of PA. We show (Section 3) that this Jervell's game is actually much stronger than PA, by showing that the critical ordinal of Jervell's game is φω (0) (while that of PA or of Kirby-Paris' Game is φ1 (0) = ?0) in the Veblen hierarchy of ordinals. 相似文献
15.
Mojgan Ghabarpoor Majid Tavassoli Kajani Masoud Allame 《Mathematical Methods in the Applied Sciences》2019,42(5):1609-1621
This paper presents a new multistep collocation method for nth order differential equations. The interval of interest is first divided into N subintervals. By determining interval conditions in Taylor interpolation in each subinterval, Taylor polynomials are calculated with different step lengths. Then the obtained solutions in each subinterval are used as initial conditions in the next step. Optimal error is assessed using Peano lemma, which shows that the errors decay by decreasing the step length. In particular, for fixed step length h, the error is of O(m?m), where m is the number of collocation points in each subinterval. Meanwhile, for fixed m, the error is of O(hm). Numerical examples demonstrate the validity and high accuracy of the proposed method even for stiff problems. 相似文献
16.
Satoru Kuroda 《Mathematical Logic Quarterly》2001,47(2):183-186
We show that length initial submodels of S12 can be extended to a model of weak second order arithmetic. As a corollary we show that the theory of length induction for polynomially bounded second order existential formulae cannot define the function division. 相似文献
17.
Andreas Weiermann 《Proceedings of the American Mathematical Society》2004,132(2):553-561
Let be a number-theoretic function. A finite set of natural numbers is called -large if . Let be the Paris Harrington statement where we replace the largeness condition by a corresponding -largeness condition. We classify those functions for which the statement is independent of first order (Peano) arithmetic . If is a fixed iteration of the binary length function, then is independent. On the other hand is provable in . More precisely let where denotes the -times iterated binary length of and denotes the inverse function of the -th member of the Hardy hierarchy. Then is independent of (for ) iff .
18.
研究了R-L导数定义下的分数维微分方程初值问题解的存在性及其唯一性,给出了方程的Peano存在定理和不等式定理,基于逐次逼近的方法,利用对分数阶R-L微夯方程构造的Tonelli序列和Ascoli引理证明分数阶R-L微分方程解的存在性,根据分数阶不等式定理证明了分数阶R-L微分方程解的唯一性. 相似文献
19.
Andrs Cordn‐Franco Alejandro Fernndez‐Margarit F. Flix Lara‐Martín 《Mathematical Logic Quarterly》2006,52(1):51-70
A well known theorem proved (independently) by J. Paris and H. Friedman states that B Σn +1 (the fragment of Arithmetic given by the collection scheme restricted to Σn +1‐formulas) is a Πn +2‐conservative extension of I Σn (the fragment given by the induction scheme restricted to Σn ‐formulas). In this paper, as a continuation of our previous work on collection schemes for Δn +1(T )‐formulas (see [4]), we study a general version of this theorem and characterize theories T such that T + B Σn +1 is a Πn +2‐conservative extension of T . We prove that this conservativeness property is equivalent to a model‐theoretic property relating Πn ‐envelopes and Πn ‐indicators for T . The analysis of Σn +1‐collection we develop here is also applied to Σn +1‐induction using Parsons' conservativeness theorem instead of Friedman‐Paris' theorem. As a corollary, our work provides new model‐theoretic proofs of two theorems of R. Kaye, J. Paris and C. Dimitracopoulos (see [8]): B Σn +1 and I Σn +1 are Σn +3‐conservative extensions of their parameter free versions, B Σ–n +1 and I Σ–n +1. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
We introduce a principle of local collection for compositional truth predicates and show that it is arithmetically conservative over the classically compositional theory of truth. This axiom states that upon restriction to formulae of any syntactic complexity, the resulting predicate satisfies full collection. In particular, arguments using collection for the truth predicate applied to sentences occurring in any given (code of a) proof do not suffice to show that the conclusion of that proof is true, in stark contrast to the case of the induction scheme.We analyse various further results concerning end-extensions of models of compositional truth and the collection scheme for the compositional truth predicate. 相似文献