No decreasing sequence of cardinals

DOI10.1007/S00153-015-0472-5zbMath1339.03038OpenAlexW2280660603MaRDI QIDQ283108

Eleftherios Tachtsis, Paul E. Howard

Publication date: 13 May 2016

Published in: Archive for Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00153-015-0472-5

zbMATH Keywords

axiom of choicecardinalsdecreasing sequence of cardinalsDedekind setsDedekind-finite setsJech-Sochor embedding theoremspermutation models of ZFAsymmetric models of ZFweak axioms of choice

Mathematics Subject Classification ID

Consistency and independence results (03E35) Axiom of choice and related propositions (03E25)

Related Items (3)

ALMOST DISJOINT AND MAD FAMILIES IN VECTOR SPACES AND CHOICE PRINCIPLES ⋮ On certain non-constructive properties of infinite-dimensional vector spaces ⋮ On a theorem of Kurepa for partially ordered sets and weak choice

Cites Work

• The dual Cantor-Bernstein theorem and the partition principle
• Set theory. An introduction to independence proofs
• Partition principles and infinite sums of cardinal numbers
• A model of set-theory in which every set of reals is Lebesgue measurable
• Cardinal addition and the axiom of choice
• An independence result concerning the axiom of choice
• The axiom of choice and linearly ordered sets
• The axiom of choice for linearly ordered families
• Weak Forms of the Axiom of Choice and the Generalized Continuum Hypothesis
• The interdependence of certain consequences of the axiom of choice
• Embedding orders into the cardinals with \mathsf DC_κ
• THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS
• The axiom of choice
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