Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Definability of initial segments   We consider implicit definability of the standard part {0,1,...} in
nonstandard models of Peano arithmetic (PA), and we ask whether there is a
model of PA in which the standard part is implicitly definable. In section 1,
we define a certain class of formulas, and show that in any model of PA the
standard part is not implicitly defined by using such formulas. In section 2 we
construct a model of PA in which the standard part is implicitly defined. To
construct such a model, first we assume a set theoretic hypothesis
diamondsuit_{S_lambda^{lambda^+}}, which is an assertion of the existence of a
very general set. Then we shall eliminate the hypothesis using absoluteness for
the existence of a model having a tree structure with a certain property.

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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph