Abstract: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.
Keywords: alternative set theory, second order arithmetic, forcing, schemes of choice, axiom of constructibility, degrees of constructibility
AMS Subject Classification: Primary 03E70; Secondary 03E25, 03E35, 03E45