Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hechler and Laver Trees   A Laver tree is a tree in which each node splits infinitely often. A Hechler
tree is a tree in which each node splits cofinitely often. We show that every
analytic set is either disjoint from the branches of a Heckler tree or contains
the branches of a Laver tree. As a corollary we deduce Silver Theorem that all
analytic sets are Ramsey. We show that in Godel's constructible universe that
our result is false for co-analytic sets (equivalently it fails for analytic
sets if we switch Hechler and Laver). We show that under Martin's axiom that
our result holds for Sigma^1_2 sets. Finally we define two games related to
this property. Latex2e 8 pages Latest version at
http://www.math.wisc.edu/~miller/res/index.html

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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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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: physics
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess