We answer some questions about graphs that are reducts of countable models of Anti-Foundation, obtained by considering the binary relation of double-membership. 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.
On double-membership graphs of models of anti-foundation / B.E.A. Adam-Day, J. Howe, R. Mennuni. - In: THE BULLETIN OF SYMBOLIC LOGIC. - ISSN 1079-8986. - 29:1(2023 Mar), pp. 128-144. [10.1017/bsl.2022.37]
On double-membership graphs of models of anti-foundation
R. MennuniUltimo
2023
Abstract
We answer some questions about graphs that are reducts of countable models of Anti-Foundation, obtained by considering the binary relation of double-membership. 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.
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