Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Forcing Axioms and the Continuum Hypothesis, part II: Transcending
  \omega_1-sequences of real numbers   The purpose of this article is to prove that the forcing axiom for completely
proper forcings is inconsistent with the Continuum Hypothesis. This answers a
longstanding problem of Shelah. The corresponding completely proper forcing
which can be constructed using CH is moreover a tree whose square is special
off the diagonal. While such trees had previously been constructed by Jensen
and Kunen under the assumption of Jensen's diamond principle, this is the first
time such a construction has been carried out using the Continuum Hypothesis.

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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph