Recursive logic frames

We define the concept of a logic frame, which extends the concept stract 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 complete (recursively compact, countably compact), if every finite (respectively: recursive, countable) consistent theory has a model. We show that for logic frames built from the cardinality quantifiers "there exists at least " completeness always implies countable compactness. On the other hand we show that a recursively compact logic frame need not be countably compact.

• Type: Journal
• Year: 2006
• Where: MLQ
• Authors: Saharon Shelah, Jouko A. Väänänen
• Keywords: Logic Frame, MLQ 2006, Recursive Logic, Recursive Logic Frame