A Negationless Interpretation of Intuitionistic Axiomatic Theories: Arithmetic and Analysis
Victor N. Krivtsov
Abstract:
A Negationless Interpretation of Intuitionistic Axiomatic Theories:
Arithmetic and Analysis
Victor N. Krivtsov
The present work contains an axiomatic treatment of some parts of the
version of intuitionistic mathematics advocated by G.F.C. Griss, the
so-called ``negationless intuitionistic mathematics''.
Formal systems NPC, NA, and FIM^N for negationless predicate logic,
arithmetic, and analysis are proposed. Our Theorem 6 in Section 2 asserts
the translatability of Heyting's arithmetic HA into NA. This result can in
fact be extended to a large class of intuitionistic theories based on HA
and their negationless counterparts.
For instance, in Section 3 this is shown for Kleene's system of intuitionistic
analysis FIM and our FIM^N.