Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New Sigma^1_3 facts   We use ``iterated square sequences'' to show: There is an L-definable
partition n: L-singulars --> omega such that if M is an inner model without 0#:
  (a) For some n, M satisfies that {alpha | n(alpha)=n} is stationary.
  (b) For each n there is a generic extension of M in which 0# does not exist
and {alpha | n(alpha)<n} is non-stationary.
  The above result is then applied to show that if M is an inner model without
0# then some Sigma^1_3 sentence not true in M can be forced over M.

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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: econ