Independence, randomness and the axiom of choice
Copyright policy )Independence, randomness and the axiom of choice
AbstractWe investigate various ways of introducing axioms for randomness in set theory. The results show that these axioms, when added to ZF, imply the failure of AC. But the axiom of extensionality plays an essential role in the derivation, and a deeper analysis may ultimately show that randomness is incompatible with extensionality.
- University of Amsterdam Netherlands
Determinacy principles, random sequences, Logic with extra quantifiers and operators, Axiom of choice and related propositions, Metamathematics of constructive systems, randomness, Axioms; other general questions in probability, intuitionistic theory of lawless sequences, Other set-theoretic hypotheses and axioms, generalized quantifier, Consistency and independence results, extensionality, data axioms
Determinacy principles, random sequences, Logic with extra quantifiers and operators, Axiom of choice and related propositions, Metamathematics of constructive systems, randomness, Axioms; other general questions in probability, intuitionistic theory of lawless sequences, Other set-theoretic hypotheses and axioms, generalized quantifier, Consistency and independence results, extensionality, data axioms
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).14 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!