Sh:790

• Shelah, S., & Väänänen, J. A. (2006). Recursive logic frames. MLQ Math. Log. Q., 52(2), 151–164. arXiv: math/0405016 DOI: 10.1002/malq.200410058 MR: 2214627
• 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.
• Version 2004-10-21_11 (28p) published version (14p)

@article{Sh:790,
 author = {Shelah, Saharon and V{\"a}{\"a}n{\"a}nen, Jouko A.},
 title = {{Recursive logic frames}},
 journal = {MLQ Math. Log. Q.},
 fjournal = {MLQ. Mathematical Logic Quarterly},
 volume = {52},
 number = {2},
 year = {2006},
 pages = {151--164},
 issn = {0942-5616},
 mrnumber = {2214627},
 mrclass = {03C80 (03C55 03C95)},
 doi = {10.1002/malq.200410058},
 note = {\href{https://arxiv.org/abs/math/0405016}{arXiv: math/0405016}},
 arxiv_number = {math/0405016}
}