AFFINE LOGIC FOR CONSTRUCTIVE MATHEMATICS

AFFINE LOGIC FOR CONSTRUCTIVE MATHEMATICS

We show that numerous distinctive concepts of constructive mathematics arise automatically from an “antithesis” translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict and...

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Veröffentlicht in:The bulletin of symbolic logic 2022-09, Vol.28 (3), p.327-386
1. Verfasser: SHULMAN, MICHAEL
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Sprache:eng
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Logic
Mathematical analysis
Mathematicians
Mathematics
Subgroups
Theorems
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description We show that numerous distinctive concepts of constructive mathematics arise automatically from an “antithesis” translation of affine logic into intuitionistic logic via a Chu/Dialectica construction. This includes apartness relations, complemented subsets, anti-subgroups and anti-ideals, strict and non-strict order pairs, cut-valued metrics, and apartness spaces. We also explain the constructive bifurcation of some classical concepts using the choice between multiplicative and additive affine connectives. Affine logic and the antithesis construction thus systematically “constructivize” classical definitions, handling the resulting bookkeeping automatically.
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subjects Logic
Mathematical analysis
Mathematicians
Mathematics
Subgroups
Theorems
title AFFINE LOGIC FOR CONSTRUCTIVE MATHEMATICS
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