Computability over arbitrary fields

  • Authors:

  • Gabor T. Herman;Stephen D. Isard

  • Affiliations:

  • IBM (U. K.) Ltd., London, England;University of Sussex, Brighton, England

  • Venue:
  • STOC '69 Proceedings of the first annual ACM symposium on Theory of computing
  • Year:
  • 1969

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Abstract

In most attempts to make precise the concept of a computable function, or decidable predicate, over a field F, it is considered necessary that the elements of F should be in some sense effectively describable, and hence that F itself should be countable. This is the attitude taken in the study of computable fields (see Rabin1). Our proposed definition of computability over arbitrary fields is based on the Shepherdson - Sturgis2 concept of an unlimited register machine.