Definable maximal independent families

Vera Fischer; Jörg Brendle; Yurii Khomskii

doi:10.1090/proc/14497

Definable maximal independent families

Vera Fischer
, Jörg Brendle
, Yurii Khomskii

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We study maximal independent families (m.i.f.) in the projective hierarchy. We show that (a) the existence of a Σ12 m.i.f. is equivalent to the existence of a II11 m.i.f., (b) in the Cohen model, there are no projective maximal independent families, and (c) in the Sacks model, there is a II11 m.i.f. We also consider a new cardinal invariant related to the question of destroying or preserving maximal independent families.

Original language	English
Pages (from-to)	3547-3557
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	147
Issue number	8
DOIs	https://doi.org/10.1090/proc/14497
Publication status	Published - 2019

Austrian Fields of Science 2012

101013 Mathematical logic

Keywords

COMBINATORICS

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10.1090/proc/14497

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abstract = "We study maximal independent families (m.i.f.) in the projective hierarchy. We show that (a) the existence of a Σ12 m.i.f. is equivalent to the existence of a II11 m.i.f., (b) in the Cohen model, there are no projective maximal independent families, and (c) in the Sacks model, there is a II11 m.i.f. We also consider a new cardinal invariant related to the question of destroying or preserving maximal independent families.",

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AB - We study maximal independent families (m.i.f.) in the projective hierarchy. We show that (a) the existence of a Σ12 m.i.f. is equivalent to the existence of a II11 m.i.f., (b) in the Cohen model, there are no projective maximal independent families, and (c) in the Sacks model, there is a II11 m.i.f. We also consider a new cardinal invariant related to the question of destroying or preserving maximal independent families.

KW - COMBINATORICS

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DO - 10.1090/proc/14497

M3 - Article

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VL - 147

SP - 3547

EP - 3557

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -

Definable maximal independent families

Abstract

Austrian Fields of Science 2012

Keywords

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