Diagonal-like embeddings
We show that the variety of diassociative loops is not finitely based even relative to power associative loops with inverse property.
A method is developed for proving non-amenability of certain automorphism groups of countable structures and is used to show that the automorphism groups of the random poset and random distributive lattice are not amenable. The universal minimal flow of the automorphism group of the random distributive lattice is computed as a canonical space of linear orderings but it is also shown that the class of finite distributive lattices does not admit hereditary order expansions with the Amalgamation Property....
We describe first-order logic elementary embeddings in a torsion-free hyperbolic group in terms of Sela’s hyperbolic towers. Thus, if embeds elementarily in a torsion free hyperbolic group , we show that the group can be obtained by successive amalgamations of groups of surfaces with boundary to a free product of with some free group and groups of closed surfaces. This gives as a corollary that an elementary subgroup of a finitely generated free group is a free factor. We also consider the...
We prove that the boolean algebras of sets definable in elementarily equivalent o-minimal expansions of real closed fields are back-and-forth equivalent, and in particular elementarily equivalent, in the language of boolean algebras with new predicates indicating the dimension, Euler characteristic and open sets. We also show that the boolean algebra of semilinear subsets of [0,1]ⁿ definable in an o-minimal expansion of a real closed field is back-and-forth equivalent to the boolean algebra of definable...