Seminar on Mathematical Logic 2005/2006; 2nd Semester Institute for Logic, Language & Computation Universiteit van Amsterdam

Goal. Students need to learn to read research papers and present mathematical ideas. The goal of this seminar is to give students an opportunity to train their reading skills in mathematics and learn how to present.

Content. Selected research papers will be handed out to the students who then have to read them, understand them and present them to the seminar.

• February 8th, 2006. Intuitionistic Set Theory.
  Speakers: Sara Uckelman, Joel Uckelman
  • Melvin C. Fitting, Intuitionistic Logic, Model Theory and Forcing, Amsterdam 1969 [Studies in Logic and the Foundations of Mathematics]; Chapter 7.
  • Andrzej Grzegorczyk, A philosophically plausible formal interpretation of intuitionistic logic, Indagationes Mathematicae 67 (1964), p. 596-601
  • Saul A. Kripke, Semantical analysis of intuitionistic logic I, in: J. N. Crossley, M. A. E. Dummett (eds.), Proceedings of the Eighth Logic Colloquium, Oxford, July 1963, Amsterdam 1965, p. 92-130
• February 15th, 2006. Forcing in Proof Theory.
  Speaker: Ansten Klev.
  • Avigad, Jeremy Forcing in proof theory, Bulletin for Symbolic Logic 10 (2004), p. 305-333
• February 22nd, 2006. Constructive Set Theory I.
  Speaker: Martijn Pennings.
  • Peter Aczel, Michael Rathjen, Notes on Constructive Set Theory, preprint; Sections 2 to 7.
  • John Myhill, Constructive set theory. Journal of Symbolic Logic 40 (1975), p. 347-382
• March 1st, 2006. Constructive Set Theory II.
  Speaker: Tyler Greene.
  • Peter Aczel, Michael Rathjen, Notes on Constructive Set Theory, preprint; Sections 8 to 11.
• March 8th, 2006. Kripke models for CZF.
  Speaker: Petter Remen.
  • Robert S. Lubarsky, Independence results around constructive ZF, Annals of Pure and Applied Logic 132 (2005), p. 209-225
• March 15th, 2006. The constructive Dedekind reals.
  Speaker: Yurii Khomskii.
  • Robert S. Lubarsky, Michael Rathjen, On the constructive Dedekind reals, preprint
• March 22nd, 2006. NO CLASS: Infinity Symposium
• March 29th, 2006. NO CLASS (Exam Week)
• April 5th, 2006. Basics of BQO Theory I.
  Speaker: Christian Kissig & Rachel Sterken.
  • Alberto Marcone, Foundations of BQO theory, Transactions of the American Mathematical Society 345 (1994), p. 641-660
  • E. C. Milner, Basic wqo- and bqo-theory, in: Ivan Rival (ed.), Graphs and order, The role of graphs in the theory of ordered sets and its applications, Proceedings of the NATO Advanced Study Institute held in Banff, Alta., May 18--31, 1984, Dordrecht 1985 [NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences 147], p. 487-501
  • Ian Hodkinson, Kruskal's Theorem and Nash-Williams theory, electronic notes
  • Link to Christian Kissigs BQO Page: This page contains the slides of Christian's and Rachel's talks and some other seminar material.
• April 12th, 2006. Basics of BQO Theory II.
  Speaker: Christian Kissig & Rachel Sterken.
• April 19th, 2006. BQOs and coinduction,
  Speaker: Daisuke Ikegami.
  • Thomas Forster, Better-quasi-orderings and coinduction, Theoretical Computer Science 309 (2003), p. 111-123
• April 26th, 2006. NO CLASS
• May 3rd, 2006. NO CLASS
• May 10th, 2006. BQO theory in modal logic.
  Speaker: Can Baskent.
  • Nick Bezhanishvili and Ian Hodkinson, All normal extensions of S5² are finitely axiomatizable, Studia Logica, 78:443-457, 2004.
• May 17th, 2006. BQO theory and the modal μ-calculus.
  Speaker: Anton Hedin.
  • Dexter Kozen, A finite model theorem for the propositional μ-calculus, Studia Logica 47(3):233-241, 1988.
• May 24th, 2006. Modal logic and (finite) model theory.
  Speaker: Raul Leal.
  • Martin Otto, Elementary Proof of the van Benthem-Rosen Characterisation Theorem, revised 2004, TUD online preprint no.2342 , May 2004, 11 pages.
• May 31st, 2006. NO CLASS (Exam Week)