The countable existentially closed pseudocomplemented semilattice

The countable existentially closed pseudocomplemented semilattice

Existentially closed CSA-groups

We study existentially closed CSA-groups. We prove that existentially closed CSA-groups without involutions are simple and divisible, and that their maximal abelian subgroups are conjugate. We also prove that every countable CSA-group without involutions embeds into a finitely generated one having the same maximal abelian subgroups, except maybe the infinite cyclic ones. We deduce from this tha...

Existentially Closed Dimension Groups

A partially ordered Abelian group M is algebraically (existentially) closed in a class C M of such structures just in case any finite system of weak inequalities (and negations of weak inequalities), defined over M, is solvable in M if solvable in some N ⊇ M in C. After characterizing existentially closed dimension groups this paper derives amalgamation properties for dimension groups, dimensio...

Existentially Closed Ii1 Factors

We examine the properties of existentially closed (R-embeddable) II1 factors. In particular, we use the fact that every automorphism of an existentially closed (R-embeddable) II1 factor is approximately inner to prove that Th(R) is not model-complete. We also show that Th(R) is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonis...

Existentially Closed BIBD Block-Intersection Graphs

A graph G with vertex set V is said to be n-existentially closed if, for every S ⊂ V with |S| = n and every T ⊆ S, there exists a vertex x ∈ V − S such that x is adjacent to each vertex of T but is adjacent to no vertex of S − T . Given a combinatorial design D with block set B, its block-intersection graph GD is the graph having vertex set B such that two vertices b1 and b2 are adjacent if and...