Summable gaps

Annals of Pure and Applied Logic 120 (1-3):1-63 (2003)
  Copy   BIBTEX

Abstract

It is proved, under Martin's Axiom, that all gaps in are indestructible in any forcing extension by a separable measure algebra. This naturally leads to a new type of gap, a summable gap. The results of these investigations have applications in Descriptive Set Theory. For example, it is shown that under Martin's Axiom the Baire categoricity of all Δ31 non-Δ31-complete sets of reals requires a weakly compact cardinal

Categories

Keywords

Reprint years

DOI

10.1016/s0168-0072(02)00034-9

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 101,553

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Fragments of Martin's axiom and δ13 sets of reals.Joan Bagaria - 1994 - Annals of Pure and Applied Logic 69 (1):1-25.
Projective forcing.Joan Bagaria & Roger Bosch - 1997 - Annals of Pure and Applied Logic 86 (3):237-266.
Applications of cohomology to set theory I: Hausdorff gaps.Daniel E. Talayco - 1995 - Annals of Pure and Applied Logic 71 (1):69-106.
Iterations of Boolean algebras with measure.Anastasis Kamburelis - 1989 - Archive for Mathematical Logic 29 (1):21-28.
Indestructibility and stationary reflection.Arthur W. Apter - 2009 - Mathematical Logic Quarterly 55 (3):228-236.
Cardinal invariants of the continuum and combinatorics on uncountable cardinals.Jörg Brendle - 2006 - Annals of Pure and Applied Logic 144 (1-3):43-72.
Distinguishing types of gaps in.Teruyuki Yorioka - 2003 - Journal of Symbolic Logic 68 (4):1261-1276.
Cardinal characteristics, projective wellorders and large continuum.Vera Fischer, Sy David Friedman & Lyubomyr Zdomskyy - 2013 - Annals of Pure and Applied Logic 164 (7-8):763-770.
Generic embeddings associated to an indestructibly weakly compact cardinal.Gunter Fuchs - 2010 - Annals of Pure and Applied Logic 162 (1):89-105.

Analytics

Added to PP
2014-01-16

Downloads
25 (#892,185)

6 months
2 (#1,696,787)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

The relative strengths of fragments of Martin's axiom.Joan Bagaria - 2024 - Annals of Pure and Applied Logic 175 (1):103330.

Add more citations

References found in this work

Internal cohen extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
Some exact equiconsistency results in set theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
Δ12-sets of reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.

View all 10 references / Add more references