PlanetMath: syntactic compactness theorem for first order logic

(more info)

Math for the people, by the people.

Main Menu

syntactic compactness theorem for first order logic

(Theorem)

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

"syntactic compactness theorem for first order logic" is owned by jihemme.

(view preamble)

Attachments:: proof of compactness theorem for first order logic (Proof) by CWoo
criterion for consistency of sets of formulas (Corollary) by jihemme
creating an infinite model (Example) by CWoo

Log in to rate this entry.
(view current ratings)

Cross-references: finite, inconsistent, sentences, first-order language
There are 3 references to this entry.

This is version 2 of syntactic compactness theorem for first order logic, born on 2002-06-04, modified 2002-06-09.
Object id is 3033, canonical name is CompactnessTheoremForFirstOrderLogic.
Accessed 3301 times total.

Classification:

AMS MSC:	03B10 (Mathematical logic and foundations :: General logic :: Classical first-order logic)
	03C07 (Mathematical logic and foundations :: Model theory :: Basic properties of first-order languages and structures)

Pending Errata and Addenda

None.

Discussion

forum policy

No messages.

Interact