1.II.16H

Logic and Set Theory | Part II, 2006

Explain what it means for a poset to be chain-complete. State Zorn's Lemma, and use it to prove that, for any two elements aa and bb of a distributive lattice LL with b↚ab \not{\leftarrow} a, there exists a lattice homomorphism f:L{0,1}f: L \rightarrow\{0,1\} with f(a)=0f(a)=0 and f(b)=1f(b)=1. Explain briefly how this result implies the completeness theorem for propositional logic.

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