Heyting-valued interpretations for constructive set theory

Nicola Gambino

doi:10.1016/j.apal.2005.05.021

Heyting-valued interpretations for constructive set theory

Nicola Gambino

Pure Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	164-188
Number of pages	25
Journal	Annals of Pure and Applied Logic
Volume	137
Issue number	1-3
DOIs	https://doi.org/10.1016/j.apal.2005.05.021
Publication status	Published - Jan 2006

Keywords

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

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10.1016/j.apal.2005.05.021

Cite this

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abstract = "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.",

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AB - 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.

KW - Constructive set theory

KW - Formal topology

KW - Pointfree topology

KW - Heyting algebra

KW - Frame

KW - Heyting-valued models

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DO - 10.1016/j.apal.2005.05.021

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SP - 164

EP - 188

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 1-3

ER -

Heyting-valued interpretations for constructive set theory

Abstract

Keywords

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