This handbook is the definitive compendium of the methods, results, and current initiatives in modern set theory in all its research directions. Set theoryhas entered its prime as an advanced and autonomous field of mathematics withfoundational significance, and the expanse and variety of this handbook attests to the richness and sophistication of the subject. The chapters are writtenby acknowledged experts, major research figures in their areas, and they eachbring to bear their experience and insights in carefully wrought, self-contained expositions. There is historical depth, elegant development, probing to the frontiers, and prospects for the future. This handbook is essential reading for the aspiring researcher, a pivotal focus for the veteran set theorist, anda massive reference for all those who want to gain a larger sense of the tremendous advances that have been made in the subject, one which first appeared as a foundation of mathematics but in the last several decades has expanded into a broad and far-reaching field with its own self-fueling initiatives. INDICE: Volume I: 0. Introduction. 1. Stationary Sets. 2. Partition Relations. 3. Coherent Sequences. 4. Borel Equivalence Relations. 5. Proper Forcing.6. Combinatorial Cardinal Characteristics of the Continuum. 7. Invariants of Measure and Category. 8. Constructibility and Class Forcing. 9. Fine Structure. 10. S* Fine Structure. Volume II: 11. Elementary Embeddings and Algebra. 12.Iterated Forcing and Elementary Embeddings. 13. Ideals and Generic ElementaryEmbeddings. 14. Cardinal Arithmetic. 15. Successors of Singular Cardinals. 16. Prikry-Type Forcings. Volume III: 17. Beginning Inner Model Theory. 18. The Covering Lemma. 19. An Outline of Inner Model Theory. 20. A Core Model Tool Box and Guide. 21. Structural Consequences of AD. 22. Determinacy in L(R). 23. Large Cardinals from Determinacy. 24. Forcing over Models of Determinacy.
- ISBN: 978-1-4020-4843-2
- Editorial: Springer
- Encuadernacion: Cartoné
- Páginas: 2150
- Fecha Publicación: 01/12/2009
- Nº Volúmenes: 3
- Idioma: Inglés