On the structure of Δ 1 4 -sets of reals
Archive for Mathematical Logic 34 (5):301-312 (1995)
Abstract
Assuming that an inaccessible cardinal exists, we construct a ZFC-model where every Δ 1 4 -set is measurable but there exists a Δ 1 4 -set without the property of Baire. By a result of Shelah, an inaccessible cardinal is necessary for this resultDOI
10.1007/bf01387510
My notes
Similar books and articles
Exact equiconsistency results for Δ 3 1 -sets of reals.Haim Judah - 1992 - Archive for Mathematical Logic 32 (2):101-112.
$triangle^1_3$-Sets of Reals.Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (1):72-80.
Martin's axioms, measurability and equiconsistency results.Jaime I. Ihoda & Saharon Shelah - 1989 - Journal of Symbolic Logic 54 (1):78-94.
On the structure of $\vec{\Delta_4^1}$ -sets of reals.Haim Judah & Otmar Spinas - 1995 - Archive for Mathematical Logic 34 (5):301-312.
Mathias absoluteness and the Ramsey property.Lorenz Halbeisen & Haim Judah - 1996 - Journal of Symbolic Logic 61 (1):177-194.
Large cardinals and projective sets.Haim Judah & Otmar Spinas - 1997 - Archive for Mathematical Logic 36 (2):137-155.
Extending Baire property by uncountably many sets.Paweł Kawa & Janusz Pawlikowski - 2010 - Journal of Symbolic Logic 75 (3):896-904.
Strongly dominating sets of reals.Michal Dečo & Miroslav Repický - 2013 - Archive for Mathematical Logic 52 (7-8):827-846.
Martin's axiom and $\Delta^2_1$ well-ordering of the reals.Uri Abraham & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):287-298.
On ideals of subsets of the plane and on Cohen reals.Jacek Cichoń & Janusz Pawlikowski - 1986 - Journal of Symbolic Logic 51 (3):560-569.
From a well-ordering of the reals it is easy (by a diagonal argument) to produce a non-determined set of reals. However, large cardinal axioms imply that all sets of reals in L (R), and more, are determined. See, for example, Neeman's papers Optimalproofs of determinacy.Andrzej S. Murawski - 1995 - Bulletin of Symbolic Logic 1:327-339.
A minimal counterexample to universal baireness.Kai Hauser - 1999 - Journal of Symbolic Logic 64 (4):1601-1627.
Cohen reals from small forcings.Janusz Pawlikowski - 2001 - Journal of Symbolic Logic 66 (1):318-324.
Analytics
Added to PP
2013-11-23
Downloads
15 (#701,025)
6 months
1 (#454,876)
2013-11-23
Downloads
15 (#701,025)
6 months
1 (#454,876)
Historical graph of downloads
References found in this work
Internal cohen extensions.D. A. Martin & R. M. Solovay - 1970 - Annals of Mathematical Logic 2 (2):143-178.
Δ12-sets of reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.
A very absolute Pi-1-2 real singleton.René David - 1982 - Annals of Mathematical Logic 23 (2-3):101-120.