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Projective Measure Without Projective Baire
About this Title
Sy David Friedman and David Schrittesser
Publication: Memoirs of the American Mathematical Society
Publication Year:
2020; Volume 267, Number 1298
ISBNs: 978-1-4704-4296-5 (print); 978-1-4704-6395-3 (online)
DOI: https://doi.org/10.1090/memo/1298
Published electronically: January 4, 2021
Keywords: Lebesgue measure,
Baire property,
projective sets,
forcing,
Mahlo cardinals
Table of Contents
Chapters
- 1. Introduction
- 2. Notation and Preliminaries
- 3. Overview of the Proof
- 4. Stratified Forcing
- 5. Easton Supported Jensen Coding
- 6. Extension and Iteration
- 7. Amalgamation
- 8. Proof of the Main Theorem
Abstract
We prove that it is consistent (relative to a Mahlo cardinal) that all projective sets of reals are Lebesgue measurable, but there is a $\Delta ^1_3$ set without the Baire property. The complexity of the set which provides a counterexample to the Baire property is optimal.- Uri Abraham, Proper forcing, Handbook of set theory. Vols. 1, 2, 3, Springer, Dordrecht, 2010, pp. 333–394. MR 2768684, DOI 10.1007/978-1-4020-5764-9_{6}
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