Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Countable support iterations and large continuum   We prove that any countable support iteration formed with posets with
$\omega_2$-p.i.c.\ has $\omega_2$-c.c., assuming CH in the ground model and
assuming also that $\omega_1$ is not collapsed. This improves earlier results
of Shelah by removing the restriction on the length of the iteration. Thus, we
solve the problem of obtaining a large continuum via such forcing iterations.

35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics