Independence Results for Finite Set Theories in Well-Founded Locally Finite Graphs

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Studia Logica:1-20 (forthcoming)
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Abstract

We consider all combinatorially possible systems corresponding to subsets of finite set theory (i.e., Zermelo-Fraenkel set theory without the axiom of infinity) and for each of them either provide a well-founded locally finite graph that is a model of that theory or show that this is impossible. To that end, we develop the technique of axiom closure of graphs.

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10.1007/s11225-023-10087-w

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Benedikt Löwe
University of Amsterdam

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The strength of Mac Lane set theory.A. R. D. Mathias - 2001 - Annals of Pure and Applied Logic 110 (1-3):107-234.
What is the theory without power set?Victoria Gitman, Joel David Hamkins & Thomas A. Johnstone - 2016 - Mathematical Logic Quarterly 62 (4-5):391-406.
Slim models of zermelo set theory.A. R. D. Mathias - 2001 - Journal of Symbolic Logic 66 (2):487-496.

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