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Topics in logic:
algebraic model theory:
finite model theory: TCT
Math 8714: Fall 2018


Syllabus



Course:
This is a course about the structure of finite
algebras from a somewhat modeltheoretic 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.


Sources:
Tame congruence theory is a localization theory
An easy way to minimal algebras, Emil Kiss,
Internat. J. Algebra Comput. 7 (1997), no. 1, 5575.
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, 67111, 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, 327356.
Algebraic Model Theory,
Bradd Hart, Alistair Lachlan, and Matthew Valeriote
Term minimal algebras, Agnes Szendrei,
Algebra Universalis 32 (1994), no. 4, 439477.
Minimal sets and varieties.
Keith Kearnes; Emil Kiss; Matthew Valeriote,
Trans. Amer. Math. Soc. 350 (1998), no. 1, 141.
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.

Dates:
Labor Day: Sep 3
Fall Break: Nov 1923
Last Day: Dec 13


