Results 51 to 60 of about 401 (159)
, 2005 According to structuralism in philosophy of mathematics, arithmetic is about a single structure. First-order theories are satisfied by (nonstandard) models that do not instantiate this structure.
Horsten, Leon +3 more
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Truth, collection and deflationism in models of peano arithmetic
, 2015 This thesis focuses on adding collection axioms to satisfaction classes and exploring the suitability of a formal deflationary truth predicate. Chapter 2 proves that every nonstandard, recursively saturated model of PA has a satisfaction class in which ...
Jones, Alexander Marcus
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Ultrafilters maximal for finite embeddability
, 2014 In this paper we study a notion of preorder that arises in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and its generalization to ultrafilters, which is related to the algebraical and topological structure
Luperi Baglini, Lorenzo (Faculty of Mathematics, Faculty of Mathematics, University of Vienna)
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Polynomial Time Computations in Models of ET
, 1982 We investigate formal notions of computations in nonstandard models of the weak arithmetic theory ET - the theory of exponential time.
Joseph, Deborah A.
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Indiscernibles and satisfaction classes in arithmetic
We investigate the theory PAI (Peano Arithmetic with Indiscernibles). Models of PAI are of the form (M, I), where M is a model of PA, I is an unbounded set of order indiscernibles over M, and (M, I) satisfies the extended induction scheme for formulae ...
Enayat, Ali,
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Preservation theorems and restricted consistency statements in bounded arithmetic
, 2004 In this article we prove preservation theorems for theories of bounded arithmetic. The following one is well-known: The ∀Π b 1 - separation of bounded arithmetic theories S i 2 from T j 2 (1 ≤ i ≤ j) is equivalent to the existence of a model of S i 2 ...
Arnold Beckmann
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, 2013 An explicit iterative algorithm to solve both linear and nonlinear problems of ordinary differential equations with initial conditions is formulated with main focus given on its comparison with some non-standard finite difference schemes. Two first order
Qureshi, Sania +3 more
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THE MINIMAL E-DEGREE PROBLEM IN FRAGMENTS OF PEANO ARITHMETIC
, 2008 . We study the minimal enumeration degree (e-degree) problem in models of fragments of Peano arithmetic (PA) and prove the following results: In any model M of Σ2 induction, there is a minimal enumeration degree if and only if M is a nonstandard model ...
M. M. Arslanov +3 more
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On counting problems in nonstandard models of Peano arithmetic with applications to groups
, 2014 Coding devices in Peano arithmetic (PA) allow complicated finite objects such as groups to be encoded in a model \(M\) ╞ PA. We call such coded objects \(M\) -finite.
Reading, Alan G
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Real closed fields and models of Peano Arithmetic
, 2010 Shepherdson [14] showed that for a discrete ordered ring I , I is a model of IOpen iff I is an integer part of a real closed ordered field. In this paper, we consider integer parts satisfying PA.
STARCHENKO S. +2 more
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