TY - JOUR
T1 - Recursive logic frames
AU - Shelah, Saharon
AU - Väänänen, Jouko
PY - 2006
Y1 - 2006
N2 - 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, N 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 N0-compactness. On the other hand we show that a recursively compact logic frame need not be N0-compact.
AB - 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, N 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 N0-compactness. On the other hand we show that a recursively compact logic frame need not be N0-compact.
KW - Compact logics
KW - Generalized quantifiers
KW - Identities
UR - http://www.scopus.com/inward/record.url?scp=33645311522&partnerID=8YFLogxK
U2 - 10.1002/malq.200410058
DO - 10.1002/malq.200410058
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AN - SCOPUS:33645311522
SN - 0942-5616
VL - 52
SP - 151
EP - 164
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
IS - 2
ER -