The pseudoarc is a co-existentially closed continuum

The Pseudoarc Is a Co-existentially Closed Continuum

Answering a question of P. Bankston, we show that the pseudoarc is a co-existentially closed continuum. We also show that C(X), for X a nondegenerate continuum, can never have quantifier elimination, answering a question of the the first and third named authors and Farah and Kirchberg.

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...

The countable existentially closed pseudocomplemented semilattice