Lecture Topics


Topics in logic: algebraic model theory: finite model theory: TCT

Math 8714: Fall 2018


This is a course about the structure of finite algebras from a somewhat model-theoretic viewpoint. Our goal is to learn the key portions of the book The Structure of Finite Algebras, along with some extensions of this theory.

Recommended background: Math 6130 and Math 6140.

  • Tame congruence theory is a localization theory
  • An easy way to minimal algebras, Emil Kiss, Internat. J. Algebra Comput. 7 (1997), no. 1, 55-75.
  • The Structure of Finite Algebras (Contemporary Mathematics) by David Hobby and Ralph McKenzie. The status of the problems from the book.
  • Some properties of finitely decidable varieties, by Matthew Valeriote and Ross Willard
  • Tame congruence theory, Matthias Clasen; Matthew Valeriote, Lectures on algebraic model theory, 67-111, Fields Inst. Monogr., 15, Amer. Math. Soc., Providence, RI, 2002.
  • Relational structure theory, a localisation theory for algebraic structures, Mike Behrisch
  • A relational localisation theory for topological algebras, Friedrich Martin Schneider
  • Composition of matrix products and categorical equivalence, Shohei Izawa, Algebra Universalis 69 (2013), no. 4, 327-356.
  • Algebraic Model Theory, Bradd Hart, Alistair Lachlan, and Matthew Valeriote
  • Term minimal algebras, Agnes Szendrei, Algebra Universalis 32 (1994), no. 4, 439-477.
  • Minimal sets and varieties. Keith Kearnes; Emil Kiss; Matthew Valeriote, Trans. Amer. Math. Soc. 350 (1998), no. 1, 1-41.
  • Structure of Decidable Locally Finite Varieties by Ralph McKenzie and Matthew Valeriote
  • Algebras, Lattices, Varieties by Ralph McKenzie, George McNulty, and Walter Taylor
  • Participation: 
    To receive a fine grade for this course, a student should ask at least one question per week.

    Labor Day: Sep 3
    Fall Break: Nov 19-23
    Last Day: Dec 13