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Recursive logic frames | | Saharon Shelah
; Jouko Väänänen
; | | Date: |
1 May 2004 | | Subject: | Logic | math.LO | | Abstract: | 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. | | Source: | arXiv, math.LO/0405016 | | Services: | Forum | Review | PDF | Favorites | |
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