Georgian Mathematical Journal 16 (2009), No. 1, 203--209
Copyright Heldermann Verlag 2009
Forcing for IZF in Sheaf Toposes
Thomas Streicher
Fachbereich Mathematik, Technische Universität, Schlossgartenstr. 7, 64289 Darmstadt, Germany
streicher@mathematik.tu-darmstadt.de
In 1985 D. Scott showed how the interpretation of intuitionistic set theory IZF in presheaf toposes can be reformulated in a more concrete fashion ā la forcing as known to set theorists. In this note we show how this can be adapted to the more general case of Grothendieck toposes dealt with abstractly by M. P. Fourman [Sheaf models for set theory, J. Pure Appl. Algebra 19(1980), 91--101] and S. Hayashi [On set theories in toposes, Logic Symposia, Hakone 1979, 1980 (Hakone, 1979/1980), 23--29, Lecture Notes in Math. 891, Springer Berlin-New York, 1981].
Keywords: Categorical logic, sheaf toposes, forcing, intuitionistic Zermelo-Fraenkel set theory, algebraic set theory.
MSC: 03E40, 03E70, 03G30, 18B25
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