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.
@article{116975, author = {Ji\v r\'\i\ Sgall and Anton\'\i n Sochor}, title = {Forcing in the alternative set theory. II}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {32}, year = {1991}, pages = {339-353}, zbl = {0751.03026}, mrnumber = {1137795}, language = {en}, url = {http://dml.mathdoc.fr/item/116975} }
Sgall, Jiří; Sochor, Antonín. Forcing in the alternative set theory. II. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 339-353. http://gdmltest.u-ga.fr/item/116975/
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