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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Acknowledgements
The authors would like to thank The World Academy of Sciences (TWAS) and the Deutsche Forschungsgemeinschaft (DFG) for their support of the project Independence phenomena in multi set theory (LO834/17-1) funding the first author’s visit at the Universität Hamburg in the spring of 2019.
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Presented by Heinrich Wansing; Received May 20, 2023.
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Balogun, F., Löwe, B. Independence Results for Finite Set Theories in Well-Founded Locally Finite Graphs. Stud Logica (2024). https://doi.org/10.1007/s11225-023-10087-w
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DOI: https://doi.org/10.1007/s11225-023-10087-w