syntactic compactness theorem for first order logic

Let $L$ be a first-order language, and $\mathrm{\Delta }\subseteq L$ be a set of sentences. If $\mathrm{\Delta }$ is inconsistent, then some finite $\mathrm{\Gamma }\subseteq \mathrm{\Delta }$ is inconsistent.

Title	syntactic compactness theorem for first order logic
Canonical name	SyntacticCompactnessTheoremForFirstOrderLogic
Date of creation	2013-03-22 12:43:59
Last modified on	2013-03-22 12:43:59
Owner	jihemme (316)
Last modified by	jihemme (316)
Numerical id	5
Author	jihemme (316)
Entry type	Theorem
Classification	msc 03B10
Classification	msc 03C07
Related topic	UpwardsSkolemLowenheimTheorem
Related topic	ProofOfUpwardsSkolemLowenheimTheorem
Related topic	GettingModelsIModelsConstructedFromConstants