Recursive logic frames

Saharon Shelah, Jouko Väänänen*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 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.

Original languageEnglish
Pages (from-to)151-164
Number of pages14
JournalMathematical Logic Quarterly
Volume52
Issue number2
DOIs
StatePublished - 2006

Keywords

  • Compact logics
  • Generalized quantifiers
  • Identities

Fingerprint

Dive into the research topics of 'Recursive logic frames'. Together they form a unique fingerprint.

Cite this