Search results for "Pointfree topology"

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Heyting-valued interpretations for Constructive Set Theory

2006

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.

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 topologyMathematicsAnnals of Pure and Applied Logic
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Spatiality for formal topologies

2007

We define what it means for a formal topology to be spatial, and investigate properties related to spatiality both in general and in examples.

Pointfree topology formal topology spatialityMathematics (miscellaneous)Theoretical computer scienceComputer scienceFormal topologyNetwork topologyComputer Science ApplicationsMathematical Structures in Computer Science
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