WHEN A RELATION with ALL BOREL SECTIONS WILL BE BOREL SOMEWHERE?

William Chan; Menachem Magidor

doi:10.1090/proc/15687

WHEN A RELATION with ALL BOREL SECTIONS WILL BE BOREL SOMEWHERE?

William Chan
, Menachem Magidor

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In ZFC, if there is a measurable cardinal with infinitely many Woodin cardinals below it, then for every binary relation R ∈ L(R) on R with all sections Δ¹₁ (Σ¹₁ or Π¹₁) and every σ-ideal I on R so that the associated forcing P_I of I⁺ Δ¹₁ subsets is proper, there exists some I⁺ Δ¹₁ set C so that R ∩ (C × R) is Δ¹₁ (Σ¹₁ or Π¹₁, respectively).

Original language	English
Pages (from-to)	833-847
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	150
Issue number	2
DOIs	https://doi.org/10.1090/proc/15687
State	Published - 2022

Bibliographical note

Publisher Copyright:
2021 American Mathematical Society

Access to Document

10.1090/proc/15687

Cite this

@article{a9637df983b444f787a2587a5fdc63ec,

title = "WHEN A RELATION with ALL BOREL SECTIONS WILL BE BOREL SOMEWHERE?",

abstract = "In ZFC, if there is a measurable cardinal with infinitely many Woodin cardinals below it, then for every binary relation R ∈ L(R) on R with all sections Δ11 (Σ11 or Π11) and every σ-ideal I on R so that the associated forcing PI of I+ Δ11 subsets is proper, there exists some I+ Δ11 set C so that R ∩ (C × R) is Δ11 (Σ11 or Π11, respectively).",

author = "William Chan and Menachem Magidor",

note = "Publisher Copyright: 2021 American Mathematical Society",

year = "2022",

doi = "10.1090/proc/15687",

language = "אנגלית",

volume = "150",

pages = "833--847",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",