Maximally Embeddable Components
arXiv:1303.2591
Abstract
We investigate the partial orderings of the form (P(X),\subset), where X is a countable binary relational structure and P(X) the set of the domains of its isomorphic substructures and show that if the components of X are maximally embeddable and satisfy an additional condition related to connectivity, then the poset (P(X),\subset) is forcing equivalent to a finite power of (P(ω)/Fin)^+, or to (P(ω\times ω)/(Fin \times Fin))^+, or to the direct product (P(Δ)/ED_fin)^+ \times ((P(ω)/Fin)^+)^n, for some n \in ω. In particular we obtain forcing equivalents of the posets of copies of countable equivalence relations, disconnected ultrahomogeneous graphs and some partial orderings.
arXiv comment17 pages, 2 figures