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Interpretations of the alternative set theory

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Summary

We show an axiom A such that there is no nontrivial interpretation of the alternative set theory (AST) inAST+A keeping ∈, sets and the class of all “standard” natural numbers. Furthermore, there is no interpretation ofAST inAST without the prolongation axiom, but there is an interpretation ofAST in the theory having the prolongation axiom and the basic set-theoretical axioms only.

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References

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Sochor, A. Interpretations of the alternative set theory. Arch Math Logic 32, 391–398 (1993). https://doi.org/10.1007/BF01270464

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  • DOI: https://doi.org/10.1007/BF01270464

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