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Heyting-valued interpretations for Constructive Set Theory
Nicola Gambinosubject
Discrete mathematicsLogicConstructive set theoryFormal topologyHeyting-valued modelsConstructive set theoryHeyting algebraConsistency (knowledge bases)ConstructiveAlgebraMathematics::LogicPointfree topologyConstructive set theory Heyting algebras independence proofsMathematics::Category TheoryComputer Science::Logic in Computer ScienceIndependence (mathematical logic)Heyting algebraFrame (artificial intelligence)FrameSet theoryFormal topologyMathematicsdescription
AbstractWe 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-01-01 | Annals of Pure and Applied Logic |