Tue, 25 Apr 2023, 1:25 pm MDT
In the first part we discuss Bjarni Jónsson's arguesian law for lattices, and its implications for lattice theory and for universal algebra. The geometric diagram in ALV2, discussed in December's talk, is explained (as was promised). We continue with some higher order arguesian identities first shown to us by Bill Lampe. The second part presents some new and old results about congruence varieties and congruence prevarieties. This part includes a discussion of commutator properties and Mal'tsev conditions. In the third part we discuss the importance of some unpublished notes of Alan Day on higher order Polin varieties and their applications to solving some problems on the collection of congruence varieties.