SPEAKER: John Mayberry (University of Bristol)
TITLE: Closure and embedding in simply infinite systems
ABSTRACT: My aim is to approach finitary arithmetic via a natural
theory of finite sets, which is proof-theoretically equivalent to
IDelta_0+exp. When Dedekind's theory of simply infinite systems is
adapted to that set theory it turns out that Dedekind's principle
result that all simply infinite systems are isomorphic no longer
holds. I shall discuss the closure and embedding properties that
obtain among the many simply infinite systems ("natural number"
systems) that arise, and point out connections with the early
levels of the Grzegorczyk hiearchy.