Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sequential and distributive forcings without choice   In $\mathsf{ZFC}$ "$\mathbb{P}$ is $\kappa$-distributive" is equivalent to
"$\mathbb{P}$ is $\kappa$-sequential". We show that this equivalence does not
hold in $\mathsf{ZF+DC_\kappa}$, but assuming the consistency of large cardinal
axioms the equivalence can still hold in the absence of choice. We also show
that while a $\kappa$-distributive forcing may violate $\mathsf{DC}$, it must
preserve $\mathsf{AC_\kappa}$; on the other hand a $\kappa$-sequential forcing
may violate $\mathsf{AC_\omega}$. We also provide a condition of
quasiproperness which is equivalent to the preservation of $\mathsf{DC}$ for
$\sigma$-sequential forcings.

5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat