Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideals and Strong Axioms of Determinacy   We show that the following two theories are equiconsistent:
  (T) ZFC, CH and "There is a dense ideal on the first uncountable cardinal
such that if j is the generic embedding associated with it then its restriction
on ordinals is independent of the generic object is". (S) ZF, ADR and "Theta is
a regular cardinal."
  The main result of this paper is that T implies that the minimal model of S
exists. Woodin, in unpublished work, showed that the consistency of S implies
the consistency of T. We will also give a proof of this result, which, together
with our main theorem, establishes the equiconsistency of T and S. Our main
result partially resolves a well-known conjecture of Woodin, and completely
solves one of the main Core Model Induction problems dating back to 90s.

14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat