This is the home page for the LFCS TPG course:
*Mathematical Structures for Semantics*.

This half course covers a variety of mathematical structures used in semantics. The course is structured around a single weekly lecture in which a selected topic is reviewed. Reading lists are issued a week in advance of lectures, and lectures assume some acquaintance with this material. Each lecture covers a different topic, and aims to reach the frontier of research in that area.

**Lectures:**
Thursdays 11-12, Room 4310

**Course starts:** Thursday 7th February

**Course ends:** Thursday 14th March

There will also be student-given lectures on miscellaneous topics in term 3.

- Thursday 7th February:
*Algebraic and continuous domains.*(Handwritten lecture note. Contact me for a copy.)- Sections 1-4 of [AJ94].

Other reading: [Sco72], [Plo83, Ch.6], [Smy83], [Jun89], [Jun90], [AR94].

- Thursday 21st February (note the postponement!):
*Recursive domain equations.*Lecture note 2- Sections 3.3 and 5 of [AJ94].

Other reading: [SP82], [Fre91], [Fre92], [Fio94], [Sim02], [Pit96].

- Thursday 28th February:
*Topological spaces from a computational perspective.*Lecture note 3- [Smy92].

Other reading: [Vic89], [Joh86], [Abr91].

- Thursday 7th March:
*Equilogical spaces.*Lecture note 4- [BBS02].

Other reading: [Sco72], [GHK80], [MS02], [Bau00].

- Thursday 14th March:
*Higher type exact real-number computation*- [BES02]

- Friday 17th May, 2-5pm, room 2509, student presentations:
- Robert Atkey:
*Coalgebras and coinduction* - Ulrich Schöpp:
*Presheaf models for concurrency* - Fedor Fomenko:
*Games models*

- Robert Atkey:

[Abr91] Samson Abramsky.
Domain theory in logical form,
* Annals of Pure and Applied Logic, *
51:1-77, 1991.

[AJ94] Samson Abramsky and Achim Jung,
Domain theory,
* Handbook of Logic in Computer Science * Vol. III, 1994.

[AR94] Jiri Adamek and Jiri Rosicky,
* Locally Presentable and Accessible Categories, *
London Mathematical Society Lecture Note Series, 189,
CUP, 1994.

[Bau00] Andrej Bauer, The Realizability Approach to Computable Analysis and Topology, PhD Thesis, CMU, 2000.

[BBS02] Andrej Bauer, Lars Birkedal and Dana Scott,
Equilogical spaces,
to appear in * Theoretical Computer Science, * 2002.

[BES02] Andrej Bauer, Martín Escardó and Alex Simpson, Comparing Functional Paradigms for Exact Real-number Computation, draft paper, 2002.

[Fio94] Marcelo Fiore,
* Axiomatic Domain Theory in Categories of Partial Maps, *
PhD Thesis, University of Edinburgh,
ECS-LFCS-94-307, 1994. (Published in Distinguished Dissertation
Series, CUP, 1996.)

[Fre91] Peter Freyd,
Algebraically complete categories,
in * Category Theory, Proceedings Como 1990, *
Springer LNM 1488, 1991.

[Fre92] Peter Freyd,
Remarks on algebraically compact categories,
in * Applications of Categories in Computer Science, *
pages 95-106, LMS Lencture Notes 177, CUP, 1992.

[GHK80] Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel,
Jimmie D. Lawson, Michael W. Mislove, and Dana S. Scott,
* A Compendium of Continuous Lattices, *
Springer-Verlag, 1980

[Joh86] Peter Johnstone,
* Stone Spaces, *
CUP, 1986.

[Jun89] Achim Jung, Cartesian Closed Categories of Domains, PhD dissertation, Vol. 66 of CWI Tracts, 1989.

[Jun90] Achim Jung,
The classification of continuous domains ,
Proc. 5th IEEE Symposium on * Logic in Computer Science, *
1990.

[MS02] Matías Menni and Alex Simpson,
Topological and Limit-space Subcategories
of Countably-based Equilogical Spaces,
To appear in * Math. Struct. in Comp. Sci.*

2002.

[Pit96] Andrew Pitts,
Relational properties of domains,
* Information and Computation, * 127:66-90, 1996.

[Plo83] Gordon Plotkin, Domains, the "Pisa notes", 1983.

[Sco72] Dana Scott, Continuous lattices, in
* Toposes, algebraic geometry and logic, * pp. 97-136,
Springer LNM 274, 1972.

[Sim02] Alex Simpson, Computational Adequacy for Recursive Types in Models of Intuitionistic Set Theory, draft paper, 2002.

[Smy83] Michael Smyth,
The largest cartesian closed category of domains,
* Theoretical Computer Science, * 27:109-119, 1983

[Smy92] Michael Smyth,
Topology,
* Handbook of Logic in Computer Science * Vol. I, 1992.

[SP82] Michael Smyth and Gordon Plotkin,
The category-theoretic solution of recursive domain equations,
* SIAM Journal of Computing, * 11:761-783, 1982.

[Vic89] Steve Vickers,
* Topology in Logical Form, *
CUP, 1989.