Strengthening known instances of Vaught Conjecture, we prove the Glimm-Effros dichotomy theorems for countable linear orderings and for simple trees. Corollaries of the theorems answer some open ...

Using an algebraic point of view we present an introduction to the groupoid theory; that is, we give fundamental properties of groupoids as uniqueness of inverses and properties of the identities and ...

An illustration of a magnifying glass. An illustration of a magnifying glass.

Abstract: Since the well-known DeMorgan theorem in two-valued logical systems may be considered as a special transformation theorem, we are interested in finding its counterpart in many-valued logical ...

Abstract: The classical isomorphism theorems for reversible Markov chains have played an important role in studying the properties of local time processes of strongly symmetric Markov processes [21], ...

We investigate the interplay between the graph isomorphism problem, logical definability, and structural graph theory on a rich family of dense graph classes: graph classes of bounded rank width. We ...

This document is my attempt to explain the fundamental homomorphism theorem for groups, starting from basic definitions. The exposition is all in the introduction of the actual document, so you can ...