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30th January, 1998: J Robin B Cockett
Computer Laboratory > Research > TSG > Logic and Semantics Seminar > 30th January, 1998: J Robin B Cockett

Speaker: J Robin B Cockett
Title: A Categorical Semantics for P-Time
Time: 30th January, 1998, 14:00
Abstract:

The universal property of a (strong) natural number object in any category with products delivers into the setting all the primitive recursive functions. It has proven difficult to obtain - in a reasonable categorical fashion - settings which have an arithmetic power below primitive recursive. However, such settings are emerging (notable Jim Otto in his PhD thesis provided a number of examples).

The purpose of this talk is to argue that finitistic universes, that is extensive categories with an internal full subcategory of finite sets, seem to provide a natural setting in which to express subrecursive arithmetics. The talk will explore some of the properties of these settings and describe how one may add arithmetic ... without adding too much arithmetic!