IF first-order logic, Kripke, and 3-valued logic. (English) Zbl 0877.03011

Sandu, Gabriel

Hintikka, Jaakko, The principles of mathematics revisited. Cambridge: Cambridge Univ. Press. 254-270 (1996).

[This paper is contained in J. Hintikka’s book: The principles of mathematics revisited (1996; Zbl 0869.03003) as an appendix.]
The author relates the definability of truth in IF first-order logic with Kripke’s result of the definability of truth in partial models. Independence friendly (IF) first-order logic and Kripke’s partial models are described, and the results concerning the definability of truth and falsity are presented and compared in a game-theoretical interpretation. The author concludes: “The result we reached here is stronger than Kripke’s given the fact that the partially interpreted IF languages are much stronger than partially interpreted first-order languages” (p. 270).
For the entire collection see [Zbl 0869.03003].

Reviewer: V.Peckhaus (Erlangen)

MSC:

03B20

Subsystems of classical logic (including intuitionistic logic)

Keywords:

independence friendly first-order logic; definability of truth; partial models; game-theoretical interpretation

Citations:

Zbl 0869.03003