P-Like Properties of Meager Ideals and Cardinal Invariants-Reference-Cited by-同舟云学术

P-Like Properties of Meager Ideals and Cardinal Invariants

Published:2023-11-01 Issue:3 Volume:85 Page:73-88
ISSN:1338-9750
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Marton Adam¹

Affiliation:

1. 1 Pavol Jozef Šafárik University in Košice , Košice , Slovakia

Abstract

Abstract We study two particular modifications of the P-property of ideals and related cardinal invariants cof𝒥 (ℐ)and cov+(ℐ). We give some results on the existence of P (𝒥)-ideals or non-P (𝒥)-ideals regarding specific classes of ideals, particularly meager ideals on ω. We also provide values of the cardinal invariant cof𝒥 (ℐ) describing the smallest families ensuring P(𝒥) for particular critical ideals. Moreover, we obtain a simple way of proving strict inequalities Fin < K 〈𝒜 〉 < K Fin × Fin for any MAD family 𝒜 using the weak P-ideal notion.

Publisher

Walter de Gruyter GmbH

Subject

General Earth and Planetary Sciences,General Environmental Science

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2023-0025

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