Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some nonstandard equivalences in Reverse Mathematics   Reverse Mathematics (RM) is a program in the foundations of mathematics
founded by Friedman and developed extensively by Simpson. The aim of RM is
finding the minimal axioms needed to prove a theorem of ordinary (i.e. non-set
theoretical) mathematics. In the majority of cases, one also obtains an
equivalence between the theorem and its minimal axioms. This equivalence is
established in a weak logical system called the base theory; four prominent
axioms which boast lots of such equivalences are dubbed mathematically natural
by Simpson. In this paper, we show that a number of axioms from Nonstandard
Analysis are equivalent to theorems of ordinary mathematics not involving
Nonstandard Analysis. These equivalences are proved in a weak base theory
recently introduced by van den Berg and the author. In particular, our base
theories have the first-order strength of elementary function arithmetic, in
contrast to the original version of this paper [22]. Our results combined with
Simpson's criterion for naturalness suggest the controversial point that
Nonstandard Analysis is actually mathematically natural.

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The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
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The categories of this paper are: eess
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex