The poset of all copies of the random graph has the 2 localization property
Abstract Let G be a countable graph containing a copy of the countable universal and homogeneous graph, also known as the random graph. Let Emb G be the monoid of self embeddings of G, P G f G f Emb G the set of copies of G contained in G, and I G the ideal of subsets of G which do not contain a copy of G. We show that the poset P G the algebra P G I G and the inverse of the right Green's pre order Emb G R have the 2 localization property. The Boolean completions of these pre orders are isomorphic and satisfy the following law: for each double sequence b n m n m o x o of elements of B n o m o b n m T Bt o o n o ph T o n 1 k n b k ph k where Bt o o denotes the set of all binary subtrees of the tree o o
Ann. Pure Appl. Log.