We show that a natural class of representable algebras (of logic) has the super amalgamation property. Applications of this results are given. In particular, questions originally posed by Tarski, Henkin, Monk and Pigozzi are answered. Several techniques for failure of various forms of the amalgamation property are appropriately modified, proving new results. Answers to open questions in the rec...

them who bestowed the faintest blessing on amalgamation and its sequela) in return, though expressions of the opposite sort, both loud and deep, are commoner than we could wish. The latest (we wish we could say it was to be the last) change', ne cessitated by that grossest of blunders, the amalgamation of the two European Armies in this country, was the reorganization of the Administrative Medi...

The paper deals with an empirical attempt to apply a variant of King’s model of optimal local government size. The debate on local government amalgamation has been particularly intensified by the economic crisis from 2008 that imposed dramatic pressures towards reduction of government expenditures. Despite the fact that the focal point of ongoing and future reforms are fiscal savings, there is ...

We prove that the genus polynomials of the graphs called iterated claws are real-rooted. This continues our work directed toward the 25-year-old conjecture that the genus distribution of every graph is log-concave. We have previously established log-concavity for sequences of graphs constructed by iterative vertexamalgamation or iterative edge-amalgamation of graphs that satisfy a commonly obse...

A state amalgamation of a directed graph is a node contraction which is only permitted under certain configurations of incident edges. In symbolic dynamics, state amalgamation and its inverse operation, state splitting, play a fundamental role in the the theory of subshifts of finite type (SFT): any conjugacy between SFTs, given as vertex shifts, can be expressed as a sequence of symbol splitti...

Using the National Longitudinal Study of Adolescent Health (Add Health), we utilize the concepts of homophily, blending, and amalgamation to describe the possible friendship patterns of multiracials. Homophily occurs when multiracials are most likely to choose other multiracials as friends. Blending occurs when friendship patterns of multiracials are somewhere in-between those of their monoraci...

We prove that independent rectangular random matrices, when embedded in a space of larger square matrices, are asymptotically free with amalgamation over a commutative finite dimensional subalgebra D (under an hypothesis of unitary invariance). Then we consider elements of a finite von Neumann algebra containing D, which have kernel and range projection in D. We associate them a free entropy wi...

We examine the properties of dependence relations in certain non-elementary classes and first-order simple theories. There are two major parts. The goal of the first part is to identify the properties of dependence relations in certain non-elementary classes that, firstly, characterize the model-theoretic properties of those classes; and secondly, allow to uniquely describe an abstract dependen...