A feasible theory of truth over combinatory algebra
- Sebastian Eberhard
- Ann. Pure Appl. Logic
Due to strictness problems, usually the syntactical definition of Frege structures is conceived as a truth theory for total applicative theories. To investigate Frege structures in a partial framework we can follow two ways. First, simply by ignoring undefinedness in the truth definition. Second, by introducing of a certain notion of pointer. Both approaches are compatible with the traditional formalizations of Frege structures and preserve the main results, namely abstraction and the proof-theoretic strength.