# Sh:790

• Shelah, S., & Väänänen, J. A. (2006). Recursive logic frames. MLQ Math. Log. Q., 52(2), 151–164.
• 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}
}