Universal Algebra Seminar

Ross Willard, Department of Pure Mathematics, University of Waterloo

"Uncountable SIs in residually small varieties in a countable signature"

Let V be a residually small variety in a countable signature.  Taylor proved that every subdirectly irreducible (SI) member of V has cardinality at most the continuum.  In 1974, McKenzie and Shelah proved that if V has an uncountable SI, then it has one whose cardinality is exactly the continuum.  Over three lectures I will present a simplified proof of this fact.  In the first lecture, I will introduce the logical framework for the proof, including the notions of pp-type and pp-saturation.

MC 5479