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
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 28,756
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.
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
Souslin Forcing.Jaime I. Ihoda & Saharon Shelah - 1988 - Journal of Symbolic Logic 53 (4):1188-1207.
Axioms of Symmetry: Throwing Darts at the Real Number Line.Chris Freiling - 1986 - Journal of Symbolic Logic 51 (1):190-200.
Mathias Absoluteness and the Ramsey Property.Lorenz Halbeisen & Haim Judah - 1996 - Journal of Symbolic Logic 61 (1):177-194.
The Largest Countable Inductive Set is a Mouse Set.Mitch Rudominer - 1999 - Journal of Symbolic Logic 64 (2):443-459.
On the Ramsey Property for Sets of Reals.Ilias G. Kastanas - 1983 - Journal of Symbolic Logic 48 (4):1035-1045.
Ramsey Sets, the Ramsey Ideal, and Other Classes Over R.Paul Corazza - 1992 - Journal of Symbolic Logic 57 (4):1441 - 1468.
▵13-Sets of Reals.Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (1):72 - 80.

Monthly downloads

Added to index

2009-01-28

Total downloads

192 ( #23,025 of 2,177,824 )

Recent downloads (6 months)

1 ( #317,245 of 2,177,824 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums