Definability and almost disjoint families

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Definability and almost disjoint families. / Törnquist, Asger Dag.

I: Advances in Mathematics, Bind 330, 2018, s. 61-73.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Törnquist, AD 2018, 'Definability and almost disjoint families', Advances in Mathematics, bind 330, s. 61-73. https://doi.org/10.1016/j.aim.2018.03.005

APA

Törnquist, A. D. (2018). Definability and almost disjoint families. Advances in Mathematics, 330, 61-73. https://doi.org/10.1016/j.aim.2018.03.005

Vancouver

Törnquist AD. Definability and almost disjoint families. Advances in Mathematics. 2018;330:61-73. https://doi.org/10.1016/j.aim.2018.03.005

Author

Törnquist, Asger Dag. / Definability and almost disjoint families. I: Advances in Mathematics. 2018 ; Bind 330. s. 61-73.

Bibtex

@article{79d0c074554646b1bebf8adc90ef6a20,
title = "Definability and almost disjoint families",
abstract = "We show that there are no infinite maximal almost disjoint ({"}mad{"}) families in Solovay's model, thus solving a long-standing problem posed by A.D.R. Mathias in 1967. We also give a new proof of Mathias' theorem that no analytic infinite almost disjoint family can be maximal, and show more generally that if Martin's Axiom holds at κ<2ℵ0, then no κ-Souslin infinite almost disjoint family can be maximal. Finally we show that if ℵL[a]1<ℵ1, then there are no Σ12[a] infinite mad families.",
author = "T{\"o}rnquist, {Asger Dag}",
year = "2018",
doi = "10.1016/j.aim.2018.03.005",
language = "English",
volume = "330",
pages = "61--73",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Definability and almost disjoint families

AU - Törnquist, Asger Dag

PY - 2018

Y1 - 2018

N2 - We show that there are no infinite maximal almost disjoint ("mad") families in Solovay's model, thus solving a long-standing problem posed by A.D.R. Mathias in 1967. We also give a new proof of Mathias' theorem that no analytic infinite almost disjoint family can be maximal, and show more generally that if Martin's Axiom holds at κ<2ℵ0, then no κ-Souslin infinite almost disjoint family can be maximal. Finally we show that if ℵL[a]1<ℵ1, then there are no Σ12[a] infinite mad families.

AB - We show that there are no infinite maximal almost disjoint ("mad") families in Solovay's model, thus solving a long-standing problem posed by A.D.R. Mathias in 1967. We also give a new proof of Mathias' theorem that no analytic infinite almost disjoint family can be maximal, and show more generally that if Martin's Axiom holds at κ<2ℵ0, then no κ-Souslin infinite almost disjoint family can be maximal. Finally we show that if ℵL[a]1<ℵ1, then there are no Σ12[a] infinite mad families.

U2 - 10.1016/j.aim.2018.03.005

DO - 10.1016/j.aim.2018.03.005

M3 - Journal article

VL - 330

SP - 61

EP - 73

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -

ID: 184033378