Fuzzy Sets and Geometric Logic

Steven Vickers

Research output: Contribution to journalArticle

4 Citations (Scopus)


Hale has identified fuzzy sets, valued in a frame (complete Heyting algebra) Omega, with certain sheaves over Omega: the subsheaves of constant sheaves. More general sheaves can be got as quotients of the fuzzy sets. His principal approach to sheaves over Omega, and topos-theoretic constructions on them, is via complete Omega-valued sets. In this paper we show how the geometric fragment of those constructions can be described in a natural "stalkwise" manner, provided one works also with incomplete Omega-valued sets. Our exposition examines in detail the interactions between different technical expressions of the notion of sheaf, and highlights a conceptual view of sheaf as "continuous set-valued map". (C) 2009 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)1175-1204
Number of pages30
JournalFuzzy Sets and Systems
Issue number9
Early online date4 Jul 2009
Publication statusPublished - 1 May 2010


  • Topos
  • Sheaf
  • Omega-valued set
  • Topology
  • Frame
  • Non-classical logics
  • Locale
  • Category theory


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