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Forcing in intuitionistic systems without power-set
Journal of Symbolic Logic 48 (3):670-682 (1983)
Abstract
It is shown how to define forcing semantics within metatheories not containing the power-set construction, in particular, how to construct exponents assuming only (a slightly strengthened form of) exponents in the metatheory. Some straightforward applications (consistency and independence results, and derived rules) are obtained for such systemsOther Versions
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Citations of this work
Wellfounded trees in categories.Ieke Moerdijk & Erik Palmgren - 2000 - Annals of Pure and Applied Logic 104 (1-3):189-218.
Heyting-valued interpretations for Constructive Set Theory.Nicola Gambino - 2006 - Annals of Pure and Applied Logic 137 (1-3):164-188.
Derived rules for predicative set theory: an application of sheaves.Benno van den Berg & Ieke Moerdijk - 2012 - Annals of Pure and Applied Logic 163 (10):1367-1383.
On some peculiar aspects of the constructive theory of point-free spaces.Giovanni Curi - 2010 - Mathematical Logic Quarterly 56 (4):375-387.
References found in this work
An interpretation of intuitionistic analysis.D. van Dalen - 1978 - Annals of Mathematical Logic 13 (1):1.
Principles of continuous choice and continuity of functions in formal systems for constructive mathematics.Michael J. Beeson - 1977 - Annals of Mathematical Logic 12 (3):249.
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