Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Largest Countable Inductive Set is a Mouse Set   Let kappa be the least ordinal alpha such that L_{alpha}(R) is admissible.
Let A be the set of reals x such that x is ordinal definable in L_{\alpha}(R),
for some alpha<kappa. It is well known that (assuming determinacy) A is the
largest countable inductive set of reals. Let T be the following theory:
  ZFC - Replacement + "There exists $\omega$ Woodin cardinals which are cofinal
in the ordinals." T has consistency strength weaker than that of the theory
  ZFC + "There exists omega Woodin cardinals", but stronger than that of the
theory
  ZFC + "There exists n Woodin Cardinals", for each n. Let M be the canonical,
minimal inner model for the theory T. In this paper we show that A is equal to
the set of reals in M. Since M is a "mouse", we say that A is a "mouse set." As
an application, we use our characterization of A to give an
inner-model-theoretic proof of Martin's theorem that A is equal to the set of
reals which are Sigma^*_n for some n.

4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn