ON DOUBLE-MEMBERSHIP GRAPHS OF MODELS OF ANTI-FOUNDATION

We answer some questions about graphs that are reducts of countable models of Anti-Foundation, obtained by considering the binary relation of double-membership $x\in y\in x$ . We show that there are continuum-many such graphs, and study their connected components. We describe their complete theories...

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Bibliographic Details
Published inThe bulletin of symbolic logic Vol. 29; no. 1; pp. 128 - 144
Main Authors ADAM-DAY, BEA, HOWE, JOHN, MENNUNI, ROSARIO
Format Journal Article
LanguageEnglish
Published New York, USA Cambridge University Press 01.03.2023
Subjects
Graphs
Set theory
03C62
non-well-founded sets
double-membership graph
reducts of set theory
03E30
Hanf’s Theorem
Anti-Foundation
membership graph
03E65
03C13
Gaifman’s Theorem
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Summary:We answer some questions about graphs that are reducts of countable models of Anti-Foundation, obtained by considering the binary relation of double-membership $x\in y\in x$ . We show that there are continuum-many such graphs, and study their connected components. We describe their complete theories and prove that each has continuum-many countable models, some of which are not reducts of models of Anti-Foundation.
ISSN:1079-8986
1943-5894
DOI:10.1017/bsl.2022.37