Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Determinacy in L(R,\mu)   Assume L(\mathbb{R},\mu) satisfies ZF+DC+\Theta>\omega_2 + \mu is a normal
fine measure on \powerset_{\omega_1}(\mathbb{R}). The main result of this paper
is the characterization theorem of L(\mathbb{R},\mu) which states that
L(\mathbb{R},\mu) satisfies \Theta>\omega_2 if and only if L(\mathbb{R},\mu)
satisfies AD^+. As a result, we obtain the equiconsistency between the two
theories: "ZFC + there are \omega^2 Woodin cardinals" and "ZF+DC+\mu is a
normal fine measure on \powerset_{\omega_1}(\mathbb{R}) + \Theta>\omega_2".

35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an