Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An integer construction of infinitesimals: Toward a theory of Eudoxus
  hyperreals   A construction of the real number system based on almost homomorphisms of the
integers Z was proposed by Schanuel, Arthan, and others. We combine such a
construction with the ultrapower or limit ultrapower construction, to construct
the hyperreals out of integers. In fact, any hyperreal field, whose universe is
a set, can be obtained by such a one-step construction directly out of
integers. Even the maximal (i.e., On-saturated) hyperreal number system
described by Kanovei and Reeken (2004) and independently by Ehrlich (2012) can
be obtained in this fashion, albeit not in NBG. In NBG, it can be obtained via
a one-step construction by means of a definable ultrapower (modulo a suitable
definable class ultrafilter).

6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas