Past exam of the computer science course of the University of Oxford / 2015 / Logic and proof / 1 / e

Table of contents
- Solution e

Solution

The propositional compactness theorem states that an arbitrary set

S

of propositional formulas is satisfiable if and only if every finite subset of

S

is satisfiable:

S has a model ⟺ every finite S_{0} \subseteq S has a model .

The satisfying Boolean valuation may depend on

S_{0}

on the right; the conclusion on the left provides one Boolean valuation satisfying all of

S

simultaneously.

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