Some combinatorial principles defined in terms of elementary submodels

• Autorzy: Sakaé Fuchino , Stefan Geschke
• Języki publikacji: EN

Abstrakty

EN

We give an equivalent, but simpler formulation of the axiom SEP, which was introduced in [9] in order to capture some of the combinatorial behaviour of models of set theory obtained by adding Cohen reals to a model of CH. Our formulation shows that many of the consequences of the weak Freese-Nation property of 𝒫(ω) studied in [6] already follow from SEP. We show that it is consistent that SEP holds while 𝒫(ω) fails to have the (ℵ₁,ℵ ₀)-ideal property introduced in [2]. This answers a question addressed independently by Fuchino and by Kunen. We also consider some natural variants of SEP and show that certain changes in the definition of SEP do not lead to a different principle, answering a question of Blass.

Kategorie tematyczne

• 03E17: Cardinal characteristics of the continuum
• 03E05: Other combinatorial set theory
• 03E65: Other hypotheses and axioms
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 181
• Numer: 3
• Strony: 233-255

Daty

wydano

2004

Twórcy

autor

Sakaé Fuchino

• Department of Natural Science and Mathematics, College of Engineering, Chubu University, Kasugai, Aichi 487-8501, Japan

autor

Stefan Geschke

• II. Mathematisches Institut, Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Germany

Identyfikatory

DOI

10.4064/fm181-3-3