A logic is said to be (κ,λ)-compact, if the following holds

If Φ is a set of sentencesMathworldPlanetmath of cardinality less than or equal to κ and all subsets of Φ of cardinality less than λ are consistent, then Φ is consistent.

For example, first order logic is (ω,ω)-compact, for if all finite subsets of some class of sentences are consistent, so is the class itself.

Title compactness
Canonical name Compactness
Date of creation 2013-03-22 13:49:34
Last modified on 2013-03-22 13:49:34
Owner Aatu (2569)
Last modified by Aatu (2569)
Numerical id 5
Author Aatu (2569)
Entry type Definition
Classification msc 03B99
Defines compactness