2004/05/01 by Saharon Shelah, Shelah, Saharon, Jouko Väänánen +2
Mathematics · #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #math.LO
paper · pdf · doi:10.48550/arxiv.math/0405016
published as MLQ Math. Log. Q. 52 No. 2 (2006) 151--164
arxiv created 2004/05/01 · openalex publication_date 2004/05/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the concept of a logic frame, which extends the concept of an abstract logic by adding the concept of a syntax and an axiom system. In a recursive logic frame the syntax and the set of axioms are recursively coded. A recursive logic frame is called recursively (countably) compact, if every recursive (respectively, countable) finitely consistent theory has a model. We show that for logic frames built from the cardinality quantifiers ''there exists at least lambda'' recursive compactness always implies countable compactness. On the other hand we show that a recursively compact extension need not be countably compact.