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On general operators binding variables in an extensional first order theory. (English) Zbl 0576.03002
The author claims that to deal with synonymy in first-order extensional languages he needed operators which took terms into terms. But in this paper he focuses on model theory for theories in languages with such operators. He presents a first-order language with operators which: take terms to wffs., wffs. to terms, terms to terms, and wffs. to wffs. He presents semantics for such a language. He then carefully shows how the Mendelson’s theorems in Ch. 2 of E. Mendelson’s ”Introduction to mathematical logic” (1966; Zbl 0192.019) can be adapted for theories in such a language.
Reviewer: C.F.Kielkopf

03B10 Classical first-order logic
03C68 Other classical first-order model theory
03C35 Categoricity and completeness of theories