# compactness of propositional logic

(30 minutes to learn)

## Summary

The Compactness Theorem of propositional logic states that if a given set of propositional sentences is contradictory, then there is also some finite subset which is contradictory.

## Context

This concept has the prerequisites:

- propositional logic
- countable sets (The proof of the Compactness Theorem makes use of countability.)

## Goals

- state the Compactness Theorem of propositional logic

- prove the Compactness Theorem

## Core resources (read/watch one of the following)

## -Paid-

→ A Mathematical Introduction to Logic

An undergraduate textbook in mathematical logic, with proofs.

Location:
Section 1.7, "Compactness and effectiveness," subsection "Compactness," pages 59-60

Additional dependencies:

- recursion theorem

## See also

-No Additional Notes-