ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

1. Logic

1991 MS Classification: Cyrus F. Nourani, METAAI and UCSB, USA Functorial Computability And Generic Definable Models Abstract We had defined infinite language categories and Functorial model theory as a specific alternative to a categorical interpretation for its logic in the categorical logic sense. From the infinite language category Lw1, B we define generic sets on Lw1, B and generic computable functors. The functor from Lw1, B to Set is an example generic functor. The functor is proved to have a limit defining positive generic models. New categorical computing areas are presented by defining functor computability and techniques for generating generic computable models. The functors define generic sets from language strings by new infinitary functorial consistency techniques, limits and models. Theorem Computbale generic functors define computable models by elementary chain limits on functorial consistent models provided the functions and relations in the language fragment are fragment definable recursive functions and relations.