We show that the class of Boolean contact algebras has the joint embedding property and the amalgamation property, and that the class of connected Boolean contact algebras has the joint embedding property but not the amalgamation property.

By in t roduc ing the concept of t he amalgamat ion of automata , we discuss their s t ruc tu re and classification in t e rms of characterist ic semigroups , w h e n the i npu t is a free semigroup generated by a set of i npu t symbols . W e demons t r a t e in this paper a direct p roduc t decomposabi l i ty of automata , and discuss the h ie rarchy of au tomata wh ich is character ized by th...

In this paper, we study amalgamations of cellular automata (CA), i.e. ways of combining two CA by disjoint union. We show that for several families of CA obtained by simple amalgamation operations (including the well-known families of majority and minority CA), the density of a large class of properties follows a zero-one law. Besides, we establish that intrinsic universality in those families ...

The questions this manuscript addresses arose in the course of an investigation of the imaginary sorts in ultraproducts of p-adic fields. These were shown to be understandable given the imaginary sorts of certain finite-dimensional vector spaces over the residue field. The residue field is pseudo-finite, and the imaginary elements there were previously studied, and shown in fact to be eliminabl...

We present a semantics for architectural specifications in Casl, including an extended static analysis compatible with model-theoretic requirements. The main obstacle here is the lack of amalgamation for Casl models. To circumvent this problem, we extend the Casl logic by introducing enriched signatures, where subsort embeddings form a category rather than just a preorder. The extended model fu...

This result follows straight from the geometric properties of þ-forking and it is nowhere near the independence theorem (which we will call “independent amalgamation”) one has in simple theories. In [?], Kim proved that the only independence relation satisfying symmetry, local character, transitivity and the independence theorem was forking in a simple theory; since there are well known example...