Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Satisfaction classes in nonstandard models of first-order arithmetic   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 saturated. A proof of this
fact is presented in detail in such a way that it is adaptable to a language
with function symbols. The idea that a satisfaction class can only see finitely
deep in a formula is extended to terms. The definition gives rise to new
notions of valuations of nonstandard terms; these are investigated. The notion
of a free satisfaction class is introduced, it is a satisfaction class free of
existential assumptions on nonstandard terms.
  It is well known that pathologies arise in some satisfaction classes. Ideas
of how to remove those are presented in the last chapter. This is done mainly
by adding inference rules to M-logic. The consistency of many of these
extensions is left as an open question.

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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th