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.
We study automorphisms in the alternative set theory. We prove that fully revealed automorphisms are not closed under composition. We also construct some special automorphisms. We generalize the notion of revealment and Sd-class.
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.
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