Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adding a random real number and its effect on Martin's axiom   We show that adding a random real number destroys a large fragment of
Martin's axiom, namely Martin's axiom for partial orders that have
precalibre-$\aleph_1$, thus answering an old question of J. Roitman [9]. We
also answer a question of J. Steprans and S. Watson [13] by showing that, by a
forcing that preserves cardinals, one can destroy the precalibre-$\aleph_1$
property of a partial ordering while preserving its ccc-ness.

15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex