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.
@article{116974, author = {Ji\v r\'\i\ Sgall}, title = {Forcing in the alternative set theory. I}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {32}, year = {1991}, pages = {323-337}, zbl = {0751.03025}, mrnumber = {1137794}, language = {en}, url = {http://dml.mathdoc.fr/item/116974} }
Sgall, Jiří. Forcing in the alternative set theory. I. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 323-337. http://gdmltest.u-ga.fr/item/116974/
Metamathematics of the Alternative set theory I, Comment. Math. Univ. Carolinae 20 (1979), 697-722. (1979) | MR 0555184 | Zbl 0433.03028
Metamathematics of the Alternative set theory II, Comment. Math. Univ. Carolinae 23 (1982), 55-79. (1982) | MR 0653351 | Zbl 0493.03030
Constructibility and shiftings of view, Comment. Math. Univ. Carolinae 26 (1985), 477-498. (1985) | MR 0817822 | Zbl 0583.03040
Scheme of choice in higher order arithmetics, to appear.
Mathematics in the Alternative Set Theory, Leipzig, 1979. | MR 0581368