Scolarité M2 (sauf MIC, MIDS)
- Mme Chatoux
- bureau 5055
- 01 57 27 93 06
- Mme Prudlo
- bureau 5055
- 01 57 27 93 06
Théorie des ensembles : Outils classiques
8 ECTS, semester 2, 12 weeks
| Program requirements | examen |
| Teacher | Boban Velikovic |
| Weekly hours | 4 h CM |
| Years | Master Logique et Fondements de l'Informatique |
Syllabus
On 8 August 1900, at the Second International Congress of Mathematicians in Paris, David Hilbert set out a list of 23 mathematical problems which, in his opinion, should serve as a guide for future research in the new century. The first problem in this list, Cantor's continuum hypothesis, was solved in two stages: by Gödel (1938) who constructed an internal model of the generalized continuum hypothesis, and by Paul Cohen (1963), who invented a model construction for the negation of Cantor's hypothesis. This course will mainly cover the two model constructions of set theory introduced by Gödel and Cohen.
Contents
- Review of basic set theory: cardinals, ordinals, partial orders, Boolean algebras, etc.
- Trees and Ramsey theory.
- models of ZFC, reflection, relativizations, ordinal definable sets.
- Gödel's constructible universe L, the consistency of the Axiom of Choice and the Continuum Hypothesis.
- Notion of forcing and generic extensions, fundamental theorem of forcing.
- Applications of forcing: the "diamond" principle, Souslin and Kurepa trees, etc.
- Iterated forcing, Martin's axiom and applications.
Bibliography
- T. JECH : Set Theory (Springer Verlag, 2002)
- P. DEHORNOY, La théorie des ensembles (Calvage et Mounet 2017)
- K. KUNEN : Set Theory (Studies in Logic : Mathematical Logic and Foundations, Vol. 34, College Publications, London, 2011)
- N. WEAVER, Forcing for mathematicians (World Scientific 2014)