Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5778403 | Advances in Mathematics | 2017 | 27 Pages |
Abstract
Let ãR,â¼ã be the Rado graph, Emb(R) the monoid of its self-embeddings, P(R)={f(R):fâEmb(R)} the set of copies of R contained in R, and IR the ideal of subsets of R which do not contain a copy of R. We consider the poset ãP(R),âã, the algebra P(R)/IR, and the inverse of the right Green's preorder on Emb(R), and show that these preorders are forcing equivalent to a two step iteration of the form PâÏ, where the poset P is similar to the Sacks perfect set forcing: adds a generic real, has the âµ0-covering property and, hence, preserves Ï1, has the Sacks property and does not produce splitting reals, while Ï codes an Ï-distributive forcing. Consequently, the Boolean completions of these four posets are isomorphic and the same holds for each countable graph containing a copy of the Rado graph.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
MiloÅ¡ S. KuriliÄ, Stevo TodorÄeviÄ,