Logic in quotes (Q1094403)

The author's technically demanding paper presupposes work of D. Gover and N. D. Belnap for the original motivation for languages and logics with a term forming quotation operator: Q( ) applying to expressions e. A quotation operator enables meta-languages and object languages to be developed in a single language with a single logic. Of course, there must be some ranking of the meta and object languages to avoid liar paradoxes. The author presents and investigates such a language. He presents a type of substitutional semantics for the language. He uses the powerful set theory \(KP+\infty\) to investigate the kind of completeness, compactness, and interpolation theorem for the non-finitely axiomatizable logic for this semantics. Amongst many other things he shows that arithmetic is an implicit definitional extension of this logic.