Previous |  Up |  Next


alternative set theory; second order arithmetic; forcing; schemes of choice; axiom of constructibility; degrees of constructibility
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.
[A] Adamowicz Z.: Constructible semi-lattices of degrees of constructibility. In: Set Theory and Hierarchy Theory V, Lecture Notes in Mathematics 619, p. 1-43. MR 0505487 | Zbl 0369.02042
[L] Lévy A.: Definability in axiomatic set theory II. In: Mathematical Logic and Foundations of Set Theory, ed. by Y. Bar-Hillel, North-Holland, 1970. MR 0268037
[S 1982] Sochor A.: Metamathematics of the alternative set theory II. Comment. Math. Univ. Carolinae 23 (1982), 55-79. MR 0653351 | Zbl 0493.03030
[S 1985] Sochor A.: Constructibility and shiftings of view. Comment. Math. Univ. Carolinae 26 (1985), 477-498. MR 0817822 | Zbl 0583.03040
[Sg] Sgall J.: Forcing in the alternative set theory I. Comment. Math. Univ. Carolinae 32 (1991), 323-337. MR 1137794 | Zbl 0751.03025
[V] Vopěnka P.: Mathematics in the Alternative Set Theory. Leipzig, 1979. MR 0581368
Partner of
EuDML logo