On the non-existence of κ -mad families

Haim Horowitz; Saharon Shelah

doi:10.1007/s00153-023-00874-6

On the non-existence of κ -mad families

Haim Horowitz^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

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

Abstract

Starting from a model with a Laver-indestructible supercompact cardinal κ , we construct a model of ZF+ DC_κ where there are no κ -mad families.

Original language	English
Pages (from-to)	1033-1039
Number of pages	7
Journal	Archive for Mathematical Logic
Volume	62
Issue number	7-8
DOIs	https://doi.org/10.1007/s00153-023-00874-6
State	Published - Nov 2023

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Keywords

Generalized descriptive set theory
Mad families
Supercompact cardinals

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10.1007/s00153-023-00874-6

Cite this

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title = "On the non-existence of κ -mad families",

abstract = "Starting from a model with a Laver-indestructible supercompact cardinal κ , we construct a model of ZF+ DCκ where there are no κ -mad families.",

keywords = "Generalized descriptive set theory, Mad families, Supercompact cardinals",

author = "Haim Horowitz and Saharon Shelah",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

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doi = "10.1007/s00153-023-00874-6",

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KW - Generalized descriptive set theory

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KW - Supercompact cardinals

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On the non-existence of κ -mad families

Abstract

Bibliographical note

Keywords

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