Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jonsson Cardinals, Erd\H{o}s Cardinals, and the Core Model   We show that every Jonsson cardinal is Ramsey in the Steel core model,
provided that this model exists and there is no model with a Woodin cardinal.
  This basic result is improved in two directions. First, we prove the same
result for delta-Jonsson and delta-Erdos cardinals, where delta is any regular
cardinal smaller than kappa. These notions correspond to Jonsson and Erdos
cardinals, except that the submodel or set of indiscernibles is only required
to have ordertype delta. The delta-Jonsson cardinals come up in the stationary
tower forcing.
  Second, we weaken the assumption that the Steel core model exists by showing
that if the universe is a generic extension of L[\vec E] and there is no model
with at Woodin cardinal then the model L[E] can take the place of the Steel
core model. It follows as a corollary that if L[\vec E] is a minimal model for
a Woodin cardinal then every delta-Jonsson cardinal in L[\vec E] is
delta-Erdos.

36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat