Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

$ Q$-sets, Sierpiński sets, and rapid filters


Authors: Haim Judah and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 111 (1991), 821-832
MSC: Primary 03E35; Secondary 54A25
MathSciNet review: 1045594
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this work we will prove the following:

Theorem 1. cons(ZF) implies cons(ZFC + there exists a $ Q$-set of reals + there exists a set of reals of cardinality $ {\aleph _1}$, which is not Lebesgue measurable).

Theorem 2. cons(ZF) implies cons(ZFC+ $ {2^{{\aleph _0}}}$ is arbitrarily larger than $ {\aleph _2}$+ there exists a Sierpinski set of cardinality $ {2^{{\aleph _0}}}$ + there are no rapid filters on $ \omega $).

These theorems give answers to questions of Fleissner [F1] and Judah [Ju].


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E35, 54A25

Retrieve articles in all journals with MSC: 03E35, 54A25


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1045594-5
PII: S 0002-9939(1991)1045594-5
Article copyright: © Copyright 1991 American Mathematical Society