Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Towers on trees

Authors: Martin Goldstern, Mark J. Johnson and Otmar Spinas
Journal: Proc. Amer. Math. Soc. 122 (1994), 557-564
MSC: Primary 03E50; Secondary 03E05, 06A07
MathSciNet review: 1284459
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that (under MA) for any $ \mathfrak{c}$ many dense sets in Laver forcing $ \mathbb{L}$ there exists a $ \sigma $-centered $ Q \subseteq \mathbb{L}$ such that all the given dense sets are dense in Q. In particular, MA implies that $ \mathbb{L}$ satisfies MA and does not collapse the continuum and the additivity of the Laver ideal is the continuum.

The same is true for Miller forcing and for Mathias forcing. In the case of Miller forcing this involves the correction of the wrong proof of Judah, Miller, and Shelah, Sacks, Laver forcing, and Martin's Axiom, Arch. Math. Logic 31 (1992), Theorem 4.1, p. 157.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E50, 03E05, 06A07

Retrieve articles in all journals with MSC: 03E50, 03E05, 06A07

Additional Information

PII: S 0002-9939(1994)1284459-3
Keywords: Laver forcing, Miller forcing, Martin's axiom, capturing density
Article copyright: © Copyright 1994 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia