Paradox and Potential Infinity

Journal of Philosophical Logic 42 (1):195-219 (2013)
Abstract
We describe a variety of sets internal to models of intuitionistic set theory that (1) manifest some of the crucial behaviors of potentially infinite sets as described in the foundational literature going back to Aristotle, and (2) provide models for systems of predicative arithmetic. We close with a brief discussion of Church’s Thesis for predicative arithmetic.
Keywords Potential infinity  Intuitionism  Predicative arithmetic  Church’s thesis
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