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ON IDEALS RELATED TO LAVER AND MILLER TREES

Part of: Set theory

Published online by Cambridge University Press:  28 August 2025

ALEKSANDER CIEŚLAK  and
ARTURO MARTÍNEZ-CELIS
ALEKSANDER CIEŚLAK*
Affiliation:
FACULTY OF PURE AND APPLIED MATHEMATICS WROCŁAW UNIVERSITY OF SCIENCE AND TECHNOLOGY WYBRZEŻE STANISŁAWA WYSPIAŃSKIEGO 27 50-370 WROCŁAW POLAND
ARTURO MARTÍNEZ-CELIS
Affiliation:
INSTYTUT MATEMATYCZNY UNIWERSYTET WROCŁAWSKI PL. GRUNWALDZKI 2 50-384 WROCŁAW POLAND E-mail: arturo.martinez-celis@math.uni.wroc.pl
*
E-mail: aleksander.cieslak@pwr.edu.pl
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Abstract

In this work, we consider the ideals $m^0(\mathcal {I})$ and $\ell ^0(\mathcal {I})$, ideals generated by the $\mathcal {I}$-positive Miller trees and $\mathcal {I}$-positive Laver trees, respectively. We investigate in which cases these ideals have cofinality larger than $\mathfrak {c}$ and we calculate some cardinal invariants closely related to these ideals.

Keywords

Marczewski idealscardinal invariantsforcingtrees

MSC classification

Primary: 03E17: Cardinal characteristics of the continuum 03E35: Consistency and independence results 03E40: Other aspects of forcing and Boolean-valued models

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Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 19
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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