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  • AFFINE LOGIC FOR CONSTRUCTIVE MATHEMATICS

  • Part of
  • MICHAEL SHULMAN
  • Journal:
    Bulletin of Symbolic Logic / Volume 28 / Issue 3 / September 2022
    Published online by Cambridge University Press:
    21 July 2022, pp. 327-386
    Print publication:
    September 2022

  • 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.