Workshop on forbidden configurations in Priestley spaces
by
Richard N. Ball
University of Denver
Coauthors: Ales Pultr (Charles University)

1. A brief review of Priestley duality, including the full-blown version.

2. Configurations. Forbidden configurations and resulting classes of distributive lattices. A few classical results and problem setting.

3. Generating first-order formulas by forbidden trees.

4. First negative result: the diamond.

5. Coproducts of Priestley spaces. Their existence and general form. The coproductivity problem.

6. Los' Theorem and closing the first cycle:

For a topped configuration P the following statements are equivalent:

• P is acyclic,

• P is coproductive,

• forbidding P in P(L) creates a first-order class of distributive lattices.

7. Aside: Prohibiting configurations and Heyting varieties.

8. Opening the second cycle: non-topped configurations and some reasons why they create more trouble.

9. The algorithm for creating first order formulas in the (acyclic) non-topped case.

10. Closing - not quite completely - the second cycle.

11. More on the structure of sums of Priestley spaces:

(a) the tame part, and details of a special case,
(b) creating (new) cycles.

12. Some open problems.

PDF

Date received: June 6, 2008