FORMAL SYSTEMS OF INTUITIONISTIC ANALYSIS, I,

Abstract

Various possible formalizations of existing intuitionistic mathematics (Heyting, Kleene, Kreisel) are compared. An axiomatization is presented that is obtained from Kreisel's by dropping the continuity axiom and adding Kripke's schema with several other innovations, the most important of which is the introduction of a new primitive idea of lawfulness symbolized by D. Roughly, Dt, where t is any kind of term, says that t is determined by a law rather than a free choice or choices. This extends to arbitrary (finite) types Kreisel's distinction between free-choice sequences and (computable) functions at the lowest type. The underlying logic is an (infinitely) many-sorted intuitionistic functional calculus with identity. Modifications of the formalization of impredicative intuitionism are given for a formalization of predicative intuitionism.

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1966
Accession Number
AD0647901

Entities

People

  • John Myhill

Organizations

  • Hughes Aircraft Company

Tags

DTIC Thesaurus Topics

  • Calculus
  • Functional Analysis
  • Identities
  • Mathematics
  • Sequences

Readers

  • Mathematical Modeling and Probability Theory.