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Recursive logic frames

✍ Scribed by Saharon Shelah; Jouko Väänänen

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
235 KB
Volume
52
Category
Article
ISSN
0044-3050

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✦ Synopsis

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, ℵ0-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 ℵ0-compactness. On the other hand we show that a recursively compact logic frame need not be ℵ0-compact.

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