Generalizing Computability Theory to Abstract Algebras
We present a survey of our work over the last four decades on generalizations of computability theory to many-sorted algebras. The following topics are discussed, among others: (1) abstract v concrete models of computation for such algebras; (2) computability and continuity, and the use of many-sorted topological partial algebras, containing the reals; (3) comparisons between various equivalent and distinct models of computability; (4) generalized Church-Turing theses.
KeywordsComputability and continuity Computability on abstract structures Computability on the reals Generalized church-turing thesis Generalized computability
We are grateful to Mark Armstrong, Sol Feferman, Diogo Poças and an anonymous referee for very helpful comments on earlier drafts of this chapter. We also thank the editors, Giovanni Sommaruga and Thomas Strahm, for the opportunity to participate in this volume, and for their helpfulness during the preparation of this chapter.
This research was supported by a grant from the Natural Sciences and Engineering Research Council (Canada).
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