Showing papers by "Gaisi Takeuti published in 1973"

Axiomatic set theory

Abstract: 1. Boolean Algebra.- 2. Generic Sets.- 3. Boolean ?-Algebras.- 4. Distributive Laws.- 5. Partial Order Structures and Topological Spaces.- 6. Boolean-Valued Structures.- 7. Relative Constructibility.- 8. Relative Constructibility and Ramified Languages.- 9. Boolean-Valued Relative Constructibility.- 10. Forcing.- 11. The Independence of V = L and the CH.- 12. independence of the AC.- 13. Boolean-Valued Set Theory.- 14. Another Interpretation of V(B).- 15. An Elementary Embedding of V[F0] in V(B).- 16. The Maximum Principle.- 17. Cardinals in V(B).- 18. Model Theoretic Consequences of the Distributive Laws.- 19. Independence Results Using the Models V(B).- 20. Weak Distributive Laws.- 21. A Proof of Marczewski's Theorem.- 22. The Completion of a Boolean Algebra.- 23. Boolean Algebras that are not Sets.- 24. Easton's Model.- Problem List.- Index of Symbols.

The ordinals of the systems of second order arithmetic with the provably Δ 2 1 -comprehension axiom and with the Δ 2 1 -comprehension axiom respectively

Abstract: Definition 1.15. A proof of second order arithmetic in the tree form formulation with G L C as its logical basis (see [5] for the precise definition) (Including substitution as one of the rules of inference) is called (3-) reducible if it satisfies the following.