Heyting-valued interpretations for constructive set theory

Research output: Contribution to journalArticlepeer-review


We define and investigate Heyting-valued interpretations for Constructive Zermelo–Frankel set theory (CZF). These interpretations provide models for CZF that are analogous to Boolean-valued models for ZF and to Heyting-valued models for IZF. Heyting-valued interpretations are defined here using set-generated frames and formal topologies. As applications of Heyting-valued interpretations, we present a relative consistency result and an independence proof.
Original languageEnglish
Pages (from-to)164-188
Number of pages25
JournalAnnals of Pure and Applied Logic
Issue number1-3
Publication statusPublished - Jan 2006


  • Constructive set theory
  • Formal topology
  • Pointfree topology
  • Heyting algebra
  • Frame
  • Heyting-valued models


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