Recursive logic frames

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 complete ( recursively compact , ℵ 0 ‐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 λ ” completeness always implies .0‐compactness. On the other hand we show that a recursively compact logic frame need not be ℵ 0 ‐compact. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)