Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How special are Cohen and random forcings i.e. Boolean algebras of the
  family of subsets of reals modulo meagre or null   The feeling that those two forcing notions-Cohen and Random-(equivalently the
corresponding Boolean algebras Borel(R)/(meager sets), Borel(R)/(null sets))
are special, was probably old and widespread. A reasonable interpretation is to
show them unique, or ``minimal'' or at least characteristic in a family of
``nice forcing'' like Borel. We shall interpret ``nice'' as Souslin as
suggested by Judah Shelah [JdSh 292]. We divide the family of Souslin forcing
to two, and expect that: among the first part, i.e. those adding some
non-dominated real, Cohen is minimal (=is below every one), while among the
rest random is quite characteristic even unique. Concerning the second class we
have weak results, concerning the first class, our results look satisfactory.
We have two main results: one (1.14) says that Cohen forcing is ``minimal'' in
the first class, the other (1.10) says that all c.c.c. Souslin forcing have a
property shared by Cohen forcing and Random real forcing, so it gives a weak
answer to the problem on how special is random forcing, but says much on all
c.c.c. Souslin forcing.

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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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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: math-ph
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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: comp-gas
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: gr-qc