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Non‐circular, non‐well‐founded set universes
Author(s) -
Tzouvaras Athanassios
Publication year - 1993
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19930390149
Subject(s) - mathematics , sequence (biology) , universe , set (abstract data type) , combinatorics , discrete mathematics , pure mathematics , astrophysics , computer science , physics , biology , genetics , programming language
We show that there are universes of sets which contain descending ϵ‐sequences of length α for every ordinal α, though they do not contain any ϵ‐cycle. It is also shown that there is no set universe containing a descending ϵ‐sequence of length On. MSC: 03E30; 03E65.
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