1999: Graduate Diploma in Distance Learning. Greek Open
University, Greece.
1987: B.Sc. University of Patras, Greece.
Research Interests:
Category Theory, Mathematical Logic
Published Papers:
1. Compact Topologies on Locally Presentable Categories, Cahiers de
Topologie et Geometrie Differentielle Categoriques, Vol. XXXVIII-3
(1997), 227-255.
2. Gabriel Topologies on Coherent Quantales, Journal of Pure and
Applied Algebra, 127(2), 177-192, 1998.
3. (with Costas
Drossos) Coupling an MV-algebra with a Boolean Algebra, Intern.
J. of Approx. Reasoning 18 (1998), 231-238.
4. Gabriel Filters and the Spectrum of an MV-algebra. In: D. Dubois et
al.(eds) Fuzzy Sets, Logics and Reasoning about Knowledge.
Kluwer, 1999.
5. Categorical Domain Theory: Scott Topology, Powercategories, Coherent
Categories ps file, Theory and Applications of Categories,
9 (2001), 106-120
6. Notions of Flatness relative to a Grothendieck Topology ps file ,Theory and Applications of Categories,
12 (2004), 225-236
7. (with J. Rosicky
and J. Velebil ),
Completeness of Cocompletions ps
file, Journal of Pure and Applied
Algebra,
196 (2005), 229-250
8. (with T.
Beke and J. Rosicky), When is Flatness Coherent?, Communications in Algebra, 33
(2
005), 1903-1912.
9. (with C. A. Drossos) A note on representing and interpreting
MV-algebras. In: S. Aguzzoli et
al.(eds) Algebraic and Proof Theoretic Aspects of MV-algebras.
Springer, LNCS 4460, pp. 119-126, 2007.
10. (with J. Velebil) Dense morphisms of monads pdf file, Theory and Applications of Categories,
18 (2007), 372-399
11. (with J. Velebil) Representability relative to a doctrine, Cahiers
de
Topologie et Geometrie Differentielle Categoriques, 50 (2009), 3-22
Preprints and notes:
1. Flatness and the left exactness of geometric realization ps file , Notes from PSSL 83, Glasgow, May 2006
2. Sifted inductive completions over cartesian closed bases pdf file , Notes from Categorical Methods in
Algebra, Topology,
Computer Science, Coimbra, October 2007
3. (with A. Matzaris and J. Velebil) Final Coalgebras in Accessible
Categories pdf file , Submitted, May 2009
Undergraduate: 1. Introduction to Algebra and Set
Theory, Fall Semester (1st year course)
Textbooks:
[1] P. Halmos, Naive Set Theory, (Greek translation) Ekkremes Editions.
[2] K. Kalfa, Introduction to Algebra, Ziti Editions
[3] D. N. Georgiou and S. Iliadis, Set Theory, Patras 2009
Old exam sheets, available as pdf files: February 08, June 09
2. Mathematical Logic, Spring
Semester (1st year course). Notes (part of a
textbook, with C. Drossos and E. Papadopetrakis). Old exam sheets,
available as pdf files: June 08,
June 09 Results (Drossos & Karazeris) September
2009
3. Mathematical Logic II
(merging of the courses tought formerly as Ordered Sets and Algebras of
Logic and Model Theory) Fall Semester (3rd year course). Course notes
in
Greek: by P. Karazeris, available as ps
file
by C. Drossos, available as pdf
file
The material covered in the course corresponds to Chapter 1, sections
2.2, 2.4, 2.5 and Chapter 3 from the first set of notes and to pages 56
to 81 from the second set of notes.
Old exam sheets, available as dvi files: September 03, February 04, February 06.
Graduate: 1. Foundations of Mathematics - Mathematical Logic, Spring
Semester.
Recommended literature:
[1] D. van Dalen, Logic and Structure,
Springer (1980)
[2] J. L. Bell and A. Slomson, Models and
Ultraproducts, North Holland (1969)
[3] A. Tzouvaras, Elements of
Mathematical Logic, Ziti Editions (1998) (in Greek)
Old exam sheets: June 04,June 06.
2. Category Theory (Reading Course), Usually available in Fall
Semester. Although it carries the weight of half a course, it is
actually taught in the form of lectures, whenever there is interest.
Students are evaluated from exercises of this and that form. Some old
notes in Greek, partly suitable for the course, are available as ps file. A higly recommended set
of notes, written by S. Awodey, has now appeared as a book (S. Awodey,
Category Theory , Oxford Logic Guides, Oxford Science Publications
2006).
Students I have
supervised (Master's Theses):
1. A. Matzaris, Completions of
Categories under Colimits and Exactness Conditions (in Greek, ps file).
2. K. Leivaditis, Characterization
of Algebraic Categories (in Greek, ps file).
3. G. Protsonis, Categories with
homotopy structure (in Greek, pdf
file).
