Results 1 to 10 of about 5,823 (137)
Satisfaction classes in nonstandard models of first-order arithmetic [PDF]
, 2002 A satisfaction class is a set of nonstandard sentences respecting Tarski's truth definition. We are mainly interested in full satisfaction classes, i.e., satisfaction classes which decides all nonstandard sentences. Kotlarski, Krajewski and Lachlan proved in 1981 that a countable model of PA admits a satisfaction class if and only if it is recursively ...
Engström, Fredrik
openaire +5 more sources
Privacy-Preserving Machine Learning With Fully Homomorphic Encryption for Deep Neural Network
IEEE Access, 2022 Fully homomorphic encryption (FHE) is a prospective tool for privacy-preserving machine learning (PPML). Several PPML models have been proposed based on various FHE schemes and approaches.
Joon-Woo Lee +10 more
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Vopěnkova Alternativní teorie množin v matematickém kánonu 20. století
Filosofický časopis, 2022 Vopěnka’s Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem’s construction of a nonstandard model of arithmetic, and its inception has been
Haniková, Zuzana
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Existentially Closed Models in the Framework of Arithmetic [PDF]
, 2016 We prove that the standard cut is definable in each existentially closed model of IΔ0 + exp by a (parameter free) П1–formula. This definition is optimal with respect to quantifier complexity and allows us to improve some previously known results on ...
Adamowicz, Zofia +2 more
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A nonstandard technique in combinatorial number theory [PDF]
, 2014 In [9], [15] it has been introduced a technique, based on nonstandard analysis, to study some problems in combinatorial number theory. In this paper we present three applications of this technique: the first one is a new proof of a known result regarding
Baglini, Lorenzo Luperi
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Scott's problem for proper Scott sets [PDF]
, 2008 I show that assuming PFA, every proper Scott set is the standard system of a model of PA. A Scott set X is proper if it is arithmetically closed and the quotient Boolean algebra X/Fin is a proper partial ...
Gitman, Victoria
core +1 more source
Axiomatics for the external numbers of nonstandard analysis [PDF]
, 2017 Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix.
Berg, Imme van den, Dinis, Bruno
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Ultrafilters maximal for finite embeddability [PDF]
, 2014 In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is related to the ...
Baglini, Lorenzo Luperi
core +3 more sources
Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory [PDF]
, 2017 The goal of this present manuscript is to introduce the reader to the nonstandard method and to provide an overview of its most prominent applications in Ramsey theory and combinatorial number theory.Comment: 126 pages.
Di Nasso, Mauro +2 more
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Stevin numbers and reality [PDF]
, 2012 We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures.
A. H. Lightstone +46 more
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