# Blog Archives

# Topic Archive: universal algebra

# Elementary equivalence of derivative structures of classical and universal algebras and second order logic

We give a survey of results in this direction for last 50-60 years (with some accents on recent results on elementary equivalence of endomorphism rings and automorphism groups of Abelian p-groups (E. I. Bunina, A. V. Mikhalev, and M. Royzner, 2013-2014).

# Algebraic and model-theoretic methods in constraint satisfaction

The Constraint Satisfaction Problem (CSP) of a first-order structure **S** in a finite relational language is the problem of deciding whether a given conjunction of atomic formulas in that language is satisfiable in **S**. Many classical computational problems can be modeled this way. The study of the complexity of CSPs involves an interesting combination of techniques from universal algebra, Ramsey theory, and model theory. I will present an overview over these techniques as well as some wild conjectures.