6 Feb 2018 Tuesday 
Lecture 9:0011:00 SP 107, F2.19 
 Definitions of lattices. The equivalence of the two definitions.
Distributive lattices (Section 13, Ch. 1 in Univ. Alg. , 2.12.6, 2.82.14, 4.4, 4.10 in Lat and Ord. We did not prove 4.10). 
6 Feb 2016 Tuesday 
Tutorial 13:0015:00 SP 107, F2.19 
 The tutorial exercises can be found here TUT 1.

8 Feb 2018 Thursday 
Lecture 13:0015:00 SP 107, F2.19 
 Distributive and modular lattices, complete lattices, Boolean lattices and Boolean algebras (Section 3 in Univ Alg,
we didn't prove Theorems 3.5 and 3.6., and Sections 4.13  4.18 in Lat and Ord).

13 Feb 2018 Tuesday 
Lecture 9:0011:00 SP 107, F2.19 
 Representation of finite Boolean algebras (5.45.7 in Lat and Ord),
Heyting algebras, equational definition, infinite distributive law, linear Heyting algebras.
(See Section 2.2.1 in here.)

13 Feb 2018 Tuesday 
Tutorial 13:0015:00 SP 107, F2.19 
 The tutorial exercises can be found here TUT 2.

15 Feb 2018 Thursday 
Lecture 13:0015:00 SP 107, F2.19 
 Heyting algebras of open sets of a topological space, Alexandroff topologies, Heyting algebras of upsets of a poset, interior algebras, topological insight on Goedel's embedding, Boolean algebra of regular open elements of a Heyting algebra, Glivenko's theorem.
A short summary can be found here Notes 1

20 Feb 2018 Tuesday 
Lecture 9:0011:00 SP 107, F2.19 
 Glivenko's theorem (sketch of the main idea), topological insight into the Goedel translation,
filters and ideals, maximal, prime and ultrafilters of Boolean algebras, Prime filter theorem (Sections 2.202.21, 10.710.18 in Lat and Ord). Note that in the lectures we worked mostly with filters, whereas Lat and Ord works mostly with ideals.

20 Feb 2018 Tuesday 
Tutorial 13:0015:00 SP 107, F2.19 
 The tutorial exercises can be found here TUT 3.

22 Feb 2018 Thursday 
Lecture 13:0015:00 SP 107, F2.19 
 Stone representation theorem (Sections 10.1510.18, 10.2010.22, 11.111.4 in Lat and Ord)

27 Feb 2018 Tuesday 
Lecture 9:0011:00 SP 107, F2.19 
 Stone duality, Congruences, homomorphic images, filters. (Sections 11.111.7).

27 Feb 2018 Tuesday 
Tutorial 13:0015:00 SP 107, F2.19 

The tutorial exercises can be found here TUT 4.

1 March Feb 2018 Thursday 
Lecture 13:0015:00 SP 107, F2.19 
 Priestley duality. (Sections 11.17  11.32 in Lat & Ord). Note that in Lat and Ord Stone spaces are called Boolean spaces.

6 March 2018 Tuesday 
Lecture 9:0011:00 SP 107, F2.19 
 Esakia duality. Alexandroff and StoneCech compactifications.
(Rough notes of the the material covered in the first 5 weeks is available on the Blackboard
page of the course, consult also Morandi notes, Sections 3 5.)

6 March 2018 Tuesday 
Tutorial 13:0015:00 SP 107, F2.19 
 The tutorial exercises can be found here TUT 5.

8 March 2018 Thursday 
Lecture 13:0015:00 SP 107, F2.19 

Universal algebras, H, S and P (Ch 2. Sections 12, Univ. Alg.), subdirectly irreducible algebras, varieties (Ch 2. Sections 89, Univ. Alg.), Birkhoff's variety theorem.
The correspondence between congruences and closed sets for distributive latices,
the correspondence between congruences and closed upsets for Heyting algebras,
Subdirectly irreducible Boolean algebras, distributive lattices and Heyting algebras. Jonsson's Lemma, finitely generated varieties.
See the course notes on Blackboard.

13 March 2018 Tuesday 
Lecture 9:0011:00 SP 107, F2.19 
 Algebraic completeness of classical and intuitionistic logics (Sections 11.11  11.16 in Lat & Ord,
consult also Section 4.3 in Notes on intuitionistic logic, and
slides 114 in Tutorial on varieties of Heyting algebras.) See also the notes on Blackboard.

13 March Feb 2018 Tuesday 
Tutorial 13:0015:00 SP 107, F2.19 
 The tutorial exercises can be found here TUT 6.

15 March 2018 Thursday 
Lecture 13:0015:00 SP 107, F2.19 
 Finitely generated varieties, finitely generated algebras, locally finite varieties, the RiegerNishimura lattice,
locally finite varieties have the FMP, Kripke complete varieties, topologically complete varieties, the FMP of HA, the McKinseyTarski theorem. (See the notes on Blackboard.)

20 March 2018 Tuesday 
Lecture 9:0011:00 SP 107, F2.19 
 Logics axiomatized by meetimplication formulas have the FMP, modal algebras,
S4algebras (also called closure algebras or interior algebras), duality for modal algebras, K4algebras and S4algebras, Esakia's lemma. See the notes on the Blackboard.

20 March Feb 2018 Tuesday 
Tutorial 13:0015:00 SP 107, F2.19 
 The tutorial exercises can be found here TUT 7.

22 March 2018 Thursday 
Lecture 13:0015:00 SP 107, F2.19 
 The connection of closure algebras and Heyting algebras, modal companions of intermediate logics, (Section 4.4 in
Notes on intuitionistic logic).
See also Modal companions.
Sahlqvist completeness theorem (see the lecture notes on Blackboard).
