Fast Track to Forcing - Mirna Dzamonja

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Résumé :
This book provides a quick yet detailed introduction to set theory and forcing, building the reader's intuition about it as well as rigorousness. Part II discusses contemporary issues in the theory of forcing, including previously unpublished results and open questions.

Biographie:
Mirna D?amonja is an Associate Member at Institut d'Histoire et de Philosophie des Sciences et des Techniques, Universit? Panth?on-Sorbonne. She works in logic, particularly set theory. The winner of a Lady Davis Fellowship and an EPSRC Advanced Fellowship, she wrote Th?orie des ensembles pour les philosophes (2017). After years as a Full University Professor, she now researches and teaches logic in various international organisations.

Sommaire:
Part I. Let's Be Independent: 1. Introduction; 2. Axiomatic Systems; 3. Zermelo-Fraenkel Axioms and the Axiom of Choice; 4. Well Orderings and Ordinals; 5. Cardinals; 6. Models and Independence; 7. Some Class Models of ZFC; 8. Forcing; 9. Violating CH; Part II. What Is New in Set Theory: 10. Introduction to Part Two; 11. Classical Extensions; 12. Iterated Forcing and Martin's Axiom; 13. Some More Large Cardinals; 14. Limitations of Martin's Axiom and Countable Supports; 15. Proper Forcing and PFA; 16. dollarsaleph_2 dollars and other Successors of Regulars; 17. Singular Cardinal Hypothesis and some PCF; 18. Forcing at Singular Cardinals and their Successors; References; Index.