Sequence of consistent sets of wifs Partially ordered Set a relation on a set s is called partial ordering or partial order if it is reflexive antisymmetric and transitive a set together with a partial ordering r is called a partially ordered set, or poset Totally Ordered Set If<s,r> is a poset and every two elements of s are comparable s is called a totally ordered set or linearly ordered set. a totally ordered set is also called a chain Lemma Let S 2C(). If <s, c> is a totally ordered set, and for any TE s, t is consistent hen U s is consistent Logic in Computer Science- p 4/21Sequence of consistent sets of wffs Partially Ordered Set A relation on a set S is called partial ordering or partial order if it is reflexive, antisymmetric and transitive. A set S together with a partial ordering R is called a partially ordered set, or poset. Totally Ordered Set If < S, R > is a poset and every two elements of S are comparable, S is called a totally ordered set or linearly ordered set. A totally ordered set is also called a chain. Lemma Let S ⊆ 2L(F). If < S, ⊆> is a totally ordered set, and for any Γ ∈ S, Γ is consistent, then S S is consistent. Logic in Computer Science – p.4/21