, Volume 42, Issue 1, pp 195-219
Date: 24 Dec 2011

Paradox and Potential Infinity

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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.

This paper is dedicated to the memory of Professor Barbara C. Scholz (1947–2011). She was first a student, later a colleague, always a friend.