Martin's axioms, measurability and equiconsistency results

Journal of Symbolic Logic 54 (1):78-94 (1989)

Abstract
We deal with the consistency strength of ZFC + variants of MA + suitable sets of reals are measurable (and/or Baire, and/or Ramsey). We improve the theorem of Harrington and Shelah [2] repairing the asymmetry between measure and category, obtaining also the same result for Ramsey. We then prove parallel theorems with weaker versions of Martin's axiom (MA(σ-centered), (MA(σ-linked)), MA(Γ + ℵ 0 ), MA(K)), getting Mahlo, inaccessible and weakly compact cardinals respectively. We prove that if there exists r ∈ R such that ω L[ r] 1 = ω 1 and MA holds, then there exists a ▵ 1 3 -selective filter on ω, and from the consistency of ZFC we build a model for ZFC + MA(I) + every ▵ 1 3 -set of reals is Lebesgue measurable, has the property of Baire and is Ramsey
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275017
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 40,066
Through your library

References found in this work BETA

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.

Add more references

Citations of this work BETA

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.
Exact Equiconsistency Results for Δ 3 1 -Sets of Reals.Haim Judah - 1992 - Archive for Mathematical Logic 32 (2):101-112.
The Stationarity of the Collection of the Locally Regulars.Gunter Fuchs - 2015 - Archive for Mathematical Logic 54 (5-6):725-739.
Summable Gaps.James Hirschorn - 2003 - Annals of Pure and Applied Logic 120 (1-3):1-63.

Add more citations

Similar books and articles

▵13-Sets of Reals.Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (1):72 - 80.
Ramsey Sets, the Ramsey Ideal, and Other Classes Over R.Paul Corazza - 1992 - Journal of Symbolic Logic 57 (4):1441 - 1468.
On the Ramsey Property for Sets of Reals.Ilias G. Kastanas - 1983 - Journal of Symbolic Logic 48 (4):1035-1045.
The Largest Countable Inductive Set is a Mouse Set.Mitch Rudominer - 1999 - Journal of Symbolic Logic 64 (2):443-459.
Mathias Absoluteness and the Ramsey Property.Lorenz Halbeisen & Haim Judah - 1996 - Journal of Symbolic Logic 61 (1):177-194.
Axioms of Symmetry: Throwing Darts at the Real Number Line.Chris Freiling - 1986 - Journal of Symbolic Logic 51 (1):190-200.
Souslin Forcing.Jaime I. Ihoda & Saharon Shelah - 1988 - Journal of Symbolic Logic 53 (4):1188-1207.

Analytics

Added to PP index
2009-01-28

Total views
198 ( #32,919 of 2,236,371 )

Recent downloads (6 months)
3 ( #585,669 of 2,236,371 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature