Overview

Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.

Full Product Details

Author:   Matthew Foreman ,  Akihiro Kanamori
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 2010
Weight:   3.382kg
ISBN:  

9789402404661

ISBN 10:   940240466
Pages:   2230
Publication Date:   23 August 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Handbook of Set Theory, Volume I, Akihiro Kanamori, 0. Introduction Thomas Jech, 1. Stationary Sets Andras Hajnal and Jean Larson, 2. Partition Relations Stevo Todorcevic, 3. Coherent Sequences Greg Hjorth, 4. Borel Equivalence Relations Uri Abraham, 5. Proper Forcing Andreas Blass, 6. Combinatorial Cardinal Characteristics of the Continuum Tomek Bartoszynski, 7. Invariants of Measure and Category Sy Friedman, 8. Constructibility and Class Forcing 48 Ralf-Dieter Schindler and Martin Zeman, 9. Fine Structure 52 Philip Welch, 10. S* Fine Structure 80 Volume II, Patrick Dehornoy, 11. Elementary Embeddings and Algebra James Cummings, 12. Iterated Forcing and Elementary Embeddings Matthew Foreman, 13. Ideals and Generic Elementary Embeddings Uri Abraham and Menachem Magidor, 14. Cardinal Arithmetic Todd Eisworth, 15. Successors of Singular Cardinals Moti Gitik, 16. Prikry-Type Forcings Volume III, William Mitchell, 17. Beginning Inner Model Theory William Mitchell, 18. The Covering Lemma John Steel, 19. An Outline of Inner Model Theory Ernest Schimmerling, 20. A Core Model Tool Box and Guide Steve Jackson, 21. Structural Consequences of AD Itay Neeman, 22. Determinacy in L(R) Peter Koellner and Hugh Woodin, 23. Large Cardinals from Determinacy Paul Larson, 24. Forcing over Models of Determinacy

Reviews

From the reviews: “This Handbook is written for graduate students and researchers … . The 24 chapters and a long introduction are written by acknowledged experts, major research figures in their areas. … The Handbook is completed by an extensive Index.”­­­ (Martin Weese, Zentralblatt MATH, Vol. 1197, 2010)

From the reviews: This Handbook is written for graduate students and researchers ... . The 24 chapters and a long introduction are written by acknowledged experts, major research figures in their areas. ... The Handbook is completed by an extensive Index. --- (Martin Weese, Zentralblatt MATH, Vol. 1197, 2010)

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions