# 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)

Bib entry

@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} }