ML-1998-06: A Negationless Interpretation of Intuitionistic Axiomatic Theories: Arithmetic and Analysis

ML-1998-06: Krivtsov, Victor N. (1998) A Negationless Interpretation of Intuitionistic Axiomatic Theories: Arithmetic and Analysis. [Report]

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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.

Item Type:	Report
Report Nr:	ML-1998-06
Series Name:	Mathematical Logic and Foundations (ML)
Year:	1998
Date Deposited:	12 Oct 2016 14:40
Last Modified:	12 Oct 2016 14:40
URI:	https://eprints.illc.uva.nl/id/eprint/1395

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