2012/01/26 by Robert A. Van Wesep, Van Wesep, Robert A.
Computer Science · Mathematics · #03B10 #03E40 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #math.LO #msc:03B10 #msc:03E40
paper · pdf · doi:10.48550/arxiv.1201.5509
openalex publication_date 2012/01/26 · arxiv created 2012/02/16 · arxiv updated 2012/02/17 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28
We develop the theory of partial satisfaction relations for structures that may be proper classes and define a satisfaction predicate appropriate to such structures. We indicate the utility of this theory as a framework for the development of the metatheory of first-order predicate logic and set theory, and we use it to prove that for any recursively enumerable extension T of ZF (Zermelo-Fraenkel set theory) there is a finitely axiomatizable extension T' of GB (von Neumann-Bernays-Gödel class theory) that is a conservative extension of T. We also prove a conservative extension result that justifies the use of this predicate to characterize ground models for forcing constructions.