BAIRE PROPERTY AND AXIOM OF CHOICE

Authors
JUDAH H SHELAH S
Citation
H. Judah et S. Shelah, BAIRE PROPERTY AND AXIOM OF CHOICE, Israel Journal of Mathematics, 84(3), 1993, pp. 435-450
Citations number
7
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Israel Journal of Mathematics → ACNP
ISSN journal
00212172
Volume
84
Issue
3
Year of publication
1993
Pages
435 - 450
Database
ISI
SICI code
0021-2172(1993)84:3<435:BPAAOC>2.0.ZU;2-8
Abstract
We show that without using inaccessible cardinals it is possible to ge t models of ''ZF + all sets of reals have the Baire property + DC(omeg a(1))'' and ''ZFC + all projective sets have the Baire property + the union of less than omega(2) many meager sets is meager'', answering tw o well-known open questions of Woodin and Judah, respectively.