Geodesic
Forcing in the alternative set theory. I
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 323-337.

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The technique of forcing is developed for the alternative set theory (AST) and similar weak theories, where it can be used to prove some new independence results. There are also introduced some new extensions of AST.
Classification : 03E25, 03E35, 03E40, 03E45, 03E70
Keywords: alternative set theory; forcing; generic extension; symmetric extension; axiom of constructibility 
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     title = {Forcing in the alternative set theory. {I}},
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Sgall, Jiří. Forcing in the alternative set theory. I. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 323-337. http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a14/