<abstract xmlns="http://www.w3.org/1999/xhtml">

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 <italic>ω</italic>. 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 &lt;<italic>K</italic> 〈𝒜 〉 &lt;<italic>K</italic> Fin <italic>×</italic> Fin for any MAD family 𝒜 using the weak P-ideal notion.
</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.

P-Like Properties of Meager Ideals and Cardinal Invariants

Pavol Jozef Šafárik University in Košice

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"P-Like Properties of Meager Ideals and Cardinal Invariants"}

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...

P-Like Properties of Meager Ideals and Cardinal Invariants

Published Online: Nov 16, 2023

Page range: 73 - 88

Received: Nov 10, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0025

Keywords
ideal, P-ideal, cardinal invariants

© 2023 Adam Marton, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

P-Like Properties of Meager Ideals and Cardinal Invariants

Published Online: Nov 16, 2023

Page range: 73 - 88

Received: Nov 10, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0025

Keywordsideal, P-ideal, cardinal invariants

© 2023 Adam Marton, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
ideal, P-ideal, cardinal invariants