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Three roads to complete lattices: orders, compatibility, polarity

  • Author(s): Holliday, Wesley Halcrow
  • et al.
Creative Commons 'BY-NC-ND' version 4.0 license
Abstract

This note aims to clarify the relations between three ways of constructing complete lattices that appear in three different areas: (1) using ordered structures, as in set-theoretic forcing, or doubly ordered structures, as in a recent semantics for intuitionistic logic; (2) using compatibility relations, as in semantics for quantum logic based on ortholattices; (3) using Birkhoff’s polarities, as in formal concept analysis.

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