Maximal almost disjoint families, determinacy, and forcing

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Standard

Maximal almost disjoint families, determinacy, and forcing. / Bakke Haga, Karen; Schrittesser, David; Törnquist, Asger.

I: Journal of Mathematical Logic, Bind 22, Nr. 1, 2150026, 2022, s. 1-42.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Bakke Haga, K, Schrittesser, D & Törnquist, A 2022, 'Maximal almost disjoint families, determinacy, and forcing', Journal of Mathematical Logic, bind 22, nr. 1, 2150026, s. 1-42. https://doi.org/10.1142/S0219061321500264

APA

Bakke Haga, K., Schrittesser, D., & Törnquist, A. (2022). Maximal almost disjoint families, determinacy, and forcing. Journal of Mathematical Logic, 22(1), 1-42. [2150026]. https://doi.org/10.1142/S0219061321500264

Vancouver

Bakke Haga K, Schrittesser D, Törnquist A. Maximal almost disjoint families, determinacy, and forcing. Journal of Mathematical Logic. 2022;22(1):1-42. 2150026. https://doi.org/10.1142/S0219061321500264

Author

Bakke Haga, Karen ; Schrittesser, David ; Törnquist, Asger. / Maximal almost disjoint families, determinacy, and forcing. I: Journal of Mathematical Logic. 2022 ; Bind 22, Nr. 1. s. 1-42.

Bibtex

@article{6861564457eb49bbaf1265910b06df78,
title = "Maximal almost disjoint families, determinacy, and forcing",
abstract = "We study the notion of -MAD families where is a Borel ideal on ω. We show that if is any finite or countably iterated Fubini product of the ideal of finite sets Fin, then there are no analytic infinite -MAD families, and assuming Projective Determinacy and Dependent Choice there are no infinite projective -MAD families; and under the full Axiom of Determinacy + V = L(a) or under AD+ there are no infinite-mad families. Similar results are obtained in Solovay's model. These results apply in particular to the ideal Fin, which corresponds to the classical notion of MAD families, as well as to the ideal Fin. The proofs combine ideas from invariant descriptive set theory and forcing. ",
keywords = "Borel ideals, Definability, determinacy, Fubini product, Mathias forcing, maximal almost disjoint families",
author = "{Bakke Haga}, Karen and David Schrittesser and Asger T{\"o}rnquist",
year = "2022",
doi = "10.1142/S0219061321500264",
language = "English",
volume = "22",
pages = "1--42",
journal = "Journal of Mathematical Logic",
issn = "0219-0613",
publisher = "World Scientific Publishing Co. Pte Ltd",
number = "1",

}

RIS

TY - JOUR

T1 - Maximal almost disjoint families, determinacy, and forcing

AU - Bakke Haga, Karen

AU - Schrittesser, David

AU - Törnquist, Asger

PY - 2022

Y1 - 2022

N2 - We study the notion of -MAD families where is a Borel ideal on ω. We show that if is any finite or countably iterated Fubini product of the ideal of finite sets Fin, then there are no analytic infinite -MAD families, and assuming Projective Determinacy and Dependent Choice there are no infinite projective -MAD families; and under the full Axiom of Determinacy + V = L(a) or under AD+ there are no infinite-mad families. Similar results are obtained in Solovay's model. These results apply in particular to the ideal Fin, which corresponds to the classical notion of MAD families, as well as to the ideal Fin. The proofs combine ideas from invariant descriptive set theory and forcing.

AB - We study the notion of -MAD families where is a Borel ideal on ω. We show that if is any finite or countably iterated Fubini product of the ideal of finite sets Fin, then there are no analytic infinite -MAD families, and assuming Projective Determinacy and Dependent Choice there are no infinite projective -MAD families; and under the full Axiom of Determinacy + V = L(a) or under AD+ there are no infinite-mad families. Similar results are obtained in Solovay's model. These results apply in particular to the ideal Fin, which corresponds to the classical notion of MAD families, as well as to the ideal Fin. The proofs combine ideas from invariant descriptive set theory and forcing.

KW - Borel ideals

KW - Definability

KW - determinacy

KW - Fubini product

KW - Mathias forcing

KW - maximal almost disjoint families

UR - http://www.scopus.com/inward/record.url?scp=85105997429&partnerID=8YFLogxK

U2 - 10.1142/S0219061321500264

DO - 10.1142/S0219061321500264

M3 - Journal article

AN - SCOPUS:85105997429

VL - 22

SP - 1

EP - 42

JO - Journal of Mathematical Logic

JF - Journal of Mathematical Logic

SN - 0219-0613

IS - 1

M1 - 2150026

ER -

ID: 276955168