6 Feb 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 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 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here TUT 12.

13 Feb 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 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 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here TUT 12.

20 Feb 2016 Monday 
Lecture 10:0012:00 SP A1.04 
 Heyting algebras, equational definition, infinite distributive law, linear Heyting algebras, Heyting algebras of open sets of a topological space.
(See Section 2.2.1 in here.)

20 Feb 2016 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here TUT 34.

27 Feb 2016 Monday 
Lecture 10:0012:00 SP A1.04 
 Heyting algebras of upsets of a partially ordered set, Alexandroff topologies, 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 Handout 1

27 Feb 2016 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here TUT 34.

6 March 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 Elements of Universal algebra: HSP, varieties, Tarski's and Birkhoff's theorems, subdirectly irreducible algebras.
A short summary can be found here Handout 2

6 March 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 56.

13 March 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 Connections between logics and varieties of algebras, LindenbaumTarski algebras, quotient algebras, superintuionistic and intermediate logics, varieties of Heyting algebras, congruences, filters and ideals of Boolean algebras (Sections 11.1111.16 and Sections 6.16.10 and 2.202.21 in Dav and Pries, for intermediate logics see Slides 1, see also the tutorial sheet 78 for the connection between logics and varieties of algebras).

13 March 2016 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 56.

20 March 2017 Tuesday 
Lecture 10:0012:00 SP A1.04 
 Maximal, prime and ultrafilters of Boolean algebras, Prime filter theorem (Sections 10.710.15 in Lat and Ord). Note that in the lectures we worked mostly with filters, whereas Lat and Ord works mostly with ideals.

20 March 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 78.

27 March 2017 Monday 
Lecture 12:0013:00 SP A1.04 
 Stone representation theorem. (Sections 11.111.4 in Lat and Ord). Note again
that in the lectures we worked with filters, whereas Lat and Ord works with ideals.

27 March 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 78.

3 April 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 Stone duality, Alexandroff and StoneCech compactifications of natural numbers (Sections 11.6  11.10 in Lat & Ord). Note that in Lat and Ord Stone spaces are called Boolean spaces.

3 April 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 910.

10 April 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 Priestley spaces, Priestley duality (Sections 11.7  11.27 in Lat & Ord). Note that in Lat and Ord Stone spaces are called Boolean spaces, also in the lectures we worked with filters, whereas Lat and Ord works with ideals.

10 April 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 910.

24 April 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 Priestley duality, Esakia spaces. (Sections 11.27  11.32 in Lat & Ord, see also the excellent notes of Pat Morandi on
Duality in lattice theory, Sections 45.)

24 April 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 1112. Please pay special attention to exercises 1 and 3.

1 May 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 Subdirectly irreducible HAs, Jonsson's Lemma (see Handout 1), the lattice of subvarieties of Var(A) for A a finite HA, locally finite varieties, The RiegerNishimura lattice, see Slides 2

1 May 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 1112. Please pay special attention to exercises 1 and 3.

8 May 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 Finitely generated varieties (i.e., verities generated by one finite algebra, locally finite varieties, finitely approximable varieties (i.e. varieties that have the FMP), the finite model property of HA, some open problems on varieties of HAs, see Slides 3

8 May 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 131415

15 May 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 Duality between modal algebras and modal spaces. Duality for K4 and S4algebras. Connection between S4algebras and Heyting algebras (see Sections 2.12.2 in Handout 3).

15 May 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 131415

22 May 2017 Monday 
Lecture 10:0012:00 SP A1.04 
 The DedekindMacNeille completions (Sections 7.36  7.44 in Lat and Ord.). We have not covered the completions of HAs. But if you are interested in this topic please consult Sections 12 in
MacNeille Completions of HAs

22 May 2017 Monday 
Tutorial 12:0013:00 SP A1.04 
 The tutorial exercises can be found here
TUT 131415
