On weak critical posets with respect to the positive definiteness of a quadratic tits form

Abstract

Let S be a finite P-critical poset, i.e., a poset that is critical with respect to the positive definiteness of a quadratic Tits form. A set S is called weakly P-critical if any infinite poset X ⊃ S contains a P-critical subset that is not isomorphic to S. We prove the existence of weakly P-critical sets. © 2008 Springer Science+Business Media, Inc.