proof of compactness theorem for first order logic


The theorem states that if a set of sentencesMathworldPlanetmath of a first-order language L is inconsistent, then some finite subset of it is inconsistent. Suppose ΔL is inconsistent. Then by definition Δ, i.e. there is a formal proof of “false” using only assumptionsPlanetmathPlanetmath from Δ. Formal proofs are finite objects, so let Γ collect all the formulasMathworldPlanetmath of Δ that are used in the proof.

Title proof of compactness theorem for first order logic
Canonical name ProofOfCompactnessTheoremForFirstOrderLogic
Date of creation 2013-03-22 12:44:02
Last modified on 2013-03-22 12:44:02
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 4
Author CWoo (3771)
Entry type Proof
Classification msc 03B10
Classification msc 03C07