Semilattice Congruences Viewed from Quasi-Orders

Quasi-orders and Semilattice Decompositions of Semigroups (A Survey)

Well - Quasi - Orders Christian

Based on Isabelle/HOL’s type class for preorders, we introduce a type class for well-quasi-orders (wqo) which is characterized by the absence of “bad” sequences (our proofs are along the lines of the proof of Nash-Williams [1], from which we also borrow terminology). Our main results are instantiations for the product type, the list type, and a type of finite trees, which (almost) directly foll...

Generalized Priestley Quasi-Orders

We introduce generalized Priestley quasi-orders and show that subalgebras of bounded distributive meet-semilattices are dually characterized by means of generalized Priestley quasi-orders. This generalizes the well-known characterization of subalgebras of bounded distributive lattices by means of Priestley quasiorders (Adams, Algebra Univers 3:216–228, 1973; Cignoli et al., Order 8(3):299– 315,...

Well-Quasi-Orders

Based on Isabelle/HOL’s type class for preorders, we introduce a type class for well-quasi-orders (wqo) which is characterized by the absence of “bad” sequences (our proofs are along the lines of the proof of Nash-Williams [1], from which we also borrow terminology). Our main results are instantiations for the product type, the list type, and a type of finite trees, which (almost) directly foll...

Universal Countable Borel quasi-Orders

In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the quasi-order of Borel reducibility. Following the approach of Louveau and Rosendal in [8] for the study of analytic equivalence relations, we study countable Bo...