Existence of consistent and maximal set Theorem LetiCl()be consistent. There existsT'EL()such that r∈I",and 2,T is consistent and maximal Zorn's Lemma Let s be a nonempty set such that for any chain Z cs, the set UZE S. Then there is a m e s which is maximal in the sense that it is not a subset of any other element of Logic in Computer Science - p 5/21Existence of consistent and maximal set Theorem Let Γ ⊆ L(F) be consistent. There exists Γ0 ∈ L(F) such that 1. Γ ⊆ Γ0, and 2. Γ0 is consistent and maximal. Zorn’s Lemma Let S be a nonempty set such that for any chain Z ⊆ S, the set S Z ∈ S. Then there is a m ∈ S which is maximal in the sense that it is not a subset of any other element of S. Logic in Computer Science – p.5/21