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.
GAMBINO, N. (2006). Heyting-valued interpretations for constructive set theory. ANNALS OF PURE AND APPLIED LOGIC, 137(1-3), 164-188 [10.1016/j.apal.2005.05.021].
Heyting-valued interpretations for constructive set theory
GAMBINO, Nicola
2006-01-01
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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