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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