Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upward closure and amalgamation in the generic multiverse of a countable
  model of set theory   I prove several theorems concerning upward closure and amalgamation in the
generic multiverse of a countable transitive model of set theory. Every such
model $W$ has forcing extensions $W[c]$ and $W[d]$ by adding a Cohen real,
which cannot be amalgamated in any further extension, but some nontrivial
forcing notions have all their extensions amalgamable. An increasing chain
$W[G_0]\subseteq W[G_1]\subseteq\cdots$ has an upper bound $W[H]$ if and only
if the forcing had uniformly bounded essential size in $W$. Every chain
$W\subseteq W[c_0]\subseteq W[c_1]\subseteq\cdots$ of extensions adding Cohen
reals is bounded above by $W[d]$ for some $W$-generic Cohen real $d$.

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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin