HIGHER INDEPENDENCE

VERA FISCHER; DIANA CAROLINA MONTOYA

doi:10.1017/jsl.2022.33

Titel

HIGHER INDEPENDENCE

Autor*in

VERA FISCHER

Institut für Mathematik, Fakultät für Mathematik, Universität Wien

DIANA CAROLINA MONTOYA

Institut für Mathematik, Fakultät für Mathematik, Universität Wien

Abstract

We study higher analogues of the classical independence number on ω . For κ regular uncountable, we denote by i(κ) the minimal size of a maximal κ -independent family. We establish ZFC relations between i(κ) and the standard higher analogues of some of the classical cardinal characteristics, e.g., r(κ)≤i(κ) and d(κ)≤i(κ) . For κ measurable, assuming that 2κ=κ+ we construct a maximal κ -independent family which remains maximal after the κ -support product of λ many copies of κ -Sacks forcing. Thus, we show the consistency of κ+=d(κ)=i(κ)<2κ . We conclude the paper with interesting open questions and discuss difficulties regarding other natural approaches to higher independence.

Stichwort

cardinal characteristicsindependent familiesgeneralised Baire spaceslarge cardinalsforcing

Objekt-Typ

journal article

Sprache

Englisch [eng]

Persistent identifier

phaidra.univie.ac.at/o:1640817

DOI

10.1017/jsl.2022.33

Erschienen in

Titel