Arithmetical realizability and basic logic
Tóm tắt
Absolute arithmetical realizability of predicate formulas is introduced. It is proved that the intuitionistic logic is not correct with this semantics, but the basic logic is correct.
Tài liệu tham khảo
S. C. Kleene, Introduction to Metamathematics (Wolters-Noordhoff, 1952; IL, Moscow, 1957).
V. E. Plisko, “Absolute Realizability of Predicate Formulas,” Izvestiya Akad. Nauk SSSR, Matem. 47 (2), 315 (1983).
W. Ruitenburg, “Basic Predicate Calculus,” Notre Dame J. Formal Logic 39 (1), 18 (1998).
S. Salehi, “Primitive Recursive Realizability and Basic Arithmetic,” Bull. Symbol. Logic 7 (1), 147 (2001).