Fiches de cours 2017-2018

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Set theory

MATH-318

Enseignant(s) :

Duparc Jacques

Langue:

English

Summary

Set Theory as a foundational system for mathematics. Relative consistency of the Axiom of Choice and the Continuum Hypothesis.

Content

Set Theory: ZFC. Extensionality and Comprehension. Relations, functions, and well-ordering. Ordinals. Class and transfinite recursion. Cardinals. Well-founded relations, Axiom of foundation, induction, and von Neumann's hierarchy. Relativization, absoluteness, reflection theorems. Gödel's constructible universe L. Axiom of Choice, and Continuum Hypothesis inside L. Po-sets, filters and generic extensions. Forcing. ZFC in generic extensions. Cohen Forcing. Independence of the Continuum Hypothesis. HOD and the Axiom of Choice: independence of the Axiom of Choice.

Keywords

Set Theory, Relative consistency, ZFC, Ordinals, Cardinals, Transfinite recursion, Relativization, Absoluteness, Constructible universe, L, Axiom of Choice, Continuum hypothesis, Forcing, Generic extensions

Learning Prerequisites

Recommended courses

Mathematical logic (or any equivalent course on first order logic). Warning: without a good understanding of first order logic, students tend to get lost sooner orl later.

Important concepts to start the course

Learning Outcomes

By the end of the course, the student must be able to:

Teaching methods

Ex cathedra lecture and exercises

Expected student activities

Assessment methods

Supervision

Office hours Yes
Assistants Yes
Forum Yes

Resources

Bibliography

  1. Thomas Jech: Set theory, Springer 2006
  2. Kenneth Kunen: Set theory, Springer, 1983
  3. Jean-Louis Krivine: Theorie des ensembles, 2007
  4. Patrick Dehornoy: Logique et théorie des ensembles; Notes de cours, FIMFA ENS: http://www.math.unicaen.fr/~dehornoy/surveys.html
  5. Yiannis Moschovakis: Notes on set theory, Springer 2006
  6. Karel Hrbacek and Thomas Jech: Introduction to Set theory, (3d edition), 1999

Ressources en bibliothèque
Websites
Moodle Link

Dans les plans d'études

Semaine de référence

 LuMaMeJeVe
8-9MAA330    
9-10    
10-11MAA330    
11-12    
12-13     
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Cours
      Exercice, TP
      Projet, autre

légende

  • Semestre d'automne
  • Session d'hiver
  • Semestre de printemps
  • Session d'été
  • Cours en français
  • Cours en anglais
  • Cours en allemand