Laurence Kirby, CUNY
Bounded finite set theory
There is a well-known close logical connection between PA and finite set theory. Is there a set theory that corresponds in an analogous way to bounded arithmetic $I\Delta_0$? I propose a candidate for such a theory, called $I\Delta_0S$, and consider the questions: what set-theoretic axioms can it prove? And given a model M of $I\Delta_0$ is there a model of $I\Delta_0S$ whose ordinals are isomorphic to M? The answer is yes if M is a model of Exp; to obtain the answer we use a new way of coding sets by numbers.