Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Borel canonization of analytic sets with Borel sections


Author: Ohad Drucker
Journal: Proc. Amer. Math. Soc. 146 (2018), 3073-3084
MSC (2010): Primary 03E15, 03E35, 03E55, 28A05, 54H05
DOI: https://doi.org/10.1090/proc/13837
Published electronically: March 30, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Kanovei, Sabok and Zapletal asked whether every proper $ \sigma $-ideal satisfies the following property: given $ E$ an analytic equivalence relation with Borel classes, there exists a set $ B$ which is Borel and $ I$-positive such that $ E\restriction _{B}$ is Borel. We propose a related problem - does every proper $ \sigma $-ideal satisfy: given $ A$ an analytic subset of the plane with Borel sections, there exists a set $ B$ which is Borel and $ I$-positive such that $ A\cap (B\times \omega ^{\omega })$ is Borel. We answer positively when a measurable cardinal exists, and negatively in $ L$, where no proper $ \sigma $ ideal has that property. We show that a positive answer for all ccc $ \sigma $-ideals implies that $ \omega _{1}$ is inaccessible to the reals and Mahlo in $ L$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 03E15, 03E35, 03E55, 28A05, 54H05

Retrieve articles in all journals with MSC (2010): 03E15, 03E35, 03E55, 28A05, 54H05


Additional Information

Ohad Drucker
Affiliation: Einstein Institute of Mathematics, Hebrew University of Jerusalem, Givat Ram. Jerusalem, 9190401, Israel

DOI: https://doi.org/10.1090/proc/13837
Received by editor(s): January 4, 2017
Received by editor(s) in revised form: May 7, 2017, and May 31, 2017
Published electronically: March 30, 2018
Additional Notes: This paper is part of the author’s PhD thesis written at the Hebrew University of Jerusalem under the supervision of Professor Menachem Magidor.
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society