Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On nonwellfounded iterated Sacks extensions, with application to the
  Glimm -- Effros property   We prove that if $\bI$ is a p.\ o. set in a countable transitive model $\gM$
of $\ZFC$ then $\gM$ can be extended by a generic sequence of reals $\a_\i,$
$\i\in\bI,$ such that $\aleph_1^\gM$ is preserved and every $\a_\i$ is Sacks
generic over $\gM[\ang{\a_\j:\j<\i}]$.
  The structure of the degrees of \dd\gM constructibility of reals in the
extension is investigated.
  As an application, we obtain a model in which the $\is12$ equivalence
relation $x \E y$ iff $\rL[x]=\rL[y]$ ($x,\,y$ are reals) does not admit a
reasonable form of the Glimm -- Effros theorem.

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The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
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The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph