proof of compactness theorem for first order logic

The theorem states that if a set of sentences of a first-order language $L$ is inconsistent, then some finite subset of it is inconsistent. Suppose $\mathrm{\Delta }\subseteq L$ is inconsistent. Then by definition $\mathrm{\Delta }⊢⟂$, i.e. there is a formal proof of “false” using only assumptions from $\mathrm{\Delta }$. Formal proofs are finite objects, so let $\mathrm{\Gamma }$ collect all the formulas of $\mathrm{\Delta }$ 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