Geodesic
Forcing in the alternative set theory. II
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 339-353

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By the technique of forcing, some new independence results are proved for the alternative set theory (AST) and similar weak theories: The scheme of choice is independent both of AST and of second order arithmetic, axiom of constructibility is independent of AST plus schemes of choice.
Classification : 03E25, 03E35, 03E40, 03E45, 03E70
Keywords: alternative set theory; second order arithmetic; forcing; schemes of choice; axiom of constructibility; degrees of constructibility 
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     author = {Sgall, Ji\v{r}{\'\i} and Sochor, Anton{\'\i}n},
     title = {Forcing in the alternative set theory. {II}},
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Sgall, Jiří; Sochor, Antonín. Forcing in the alternative set theory. II. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 2, pp. 339-353. http://geodesic.mathdoc.fr/item/CMUC_1991__32_2_a15/