On the existence of almost disjoint and MAD families without $\mathsf {AC}$

DOI10.4064/ba8148-3-2019zbMath1477.03200OpenAlexW2947012170MaRDI QIDQ5207289

Eleftherios Tachtsis

Publication date: 19 December 2019

Published in: Bulletin of the Polish Academy of Sciences Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/ba8148-3-2019

zbMATH Keywords

axiom of choiceweak axioms of choicealmost disjoint familyPincus' transfer theoremsMAD familyJech-Sochor first embedding theoremmodels of ZFA and ZF

Mathematics Subject Classification ID

Consistency and independence results (03E35) Other combinatorial set theory (03E05) Axiom of choice and related propositions (03E25)

Related Items

ALMOST DISJOINT AND MAD FAMILIES IN VECTOR SPACES AND CHOICE PRINCIPLES ⋮ The Boolean prime ideal theorem does not imply the extension of almost disjoint families to MAD families

Cites Work

• Unnamed Item
• Infinite permutation groups. II: Subgroups of small index
• Dedekind-Endlichkeit und Wohlordenbarkeit
• Definability and almost disjoint families
• On the non-existence of mad families
• Well ordered subsets of linearly ordered sets
• On the Existence of Free Ultrafilters on ω and on Russell-sets in ZF
• SUBGROUPS OF SMALL INDEX IN ORDERED PERMUTATION GROUPS
• Adding dependent choice
• Happy families
• Axioms of multiple choice
• The axiom of choice