Summary
We show that a consistent, finitely axiomatized, sequential theory cannot prove its own inconsistency on every definable cut. A corollary is that there are at least three degrees of global interpretability of theories equivalent modulo local interpretability to a consistent, finitely axiomatized, sequential theory U.
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Visser, A. The unprovability of small inconsistency. Arch Math Logic 32, 275–298 (1993). https://doi.org/10.1007/BF01387407
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DOI: https://doi.org/10.1007/BF01387407