Combinatorial set theory: partition relations for cardinals

Medientyp: E-Book

Titel: Combinatorial set theory : partition relations for cardinals

Enthält: Front Cover; Combinatorial Set Theory: Partition Relations for Cardinals; Copyright Page; Contents; Preface; Chapter I. Introduction; 1. Notation and basic concepts; 2. The axioms of Zermelo-Fraenkel set theory; 3. Ordinals cardinals, and order types; 4. Basic tools of set theory; Chapter II. Preliminaries; 5. Stationary sets; 6. Equalities and inequalities for cardinals; 7. The logarithm operation; Chapter III. Fundamentals about partition relations; 8. A guide to partition symbols; 9. Elementary properties of the ordinary partition symbol; 10. Ramsey's theorem
11. The Erdös-Dushnik-Miller theorem12. Negative relations with infinite superscripts; Chapter IV. Trees and positive ordinary partition relations; 13.Trees; 14. Tree arguments; 15. End-homogeneous sets; 16. The Stepping-up Lemma; 17. The main results in case r = 2 and k is regular; and some corollaries for r G 3; 18. A direct construction of the canonical partition tree; Chapter V. Negative ordinary partition relations, and the discussion of the finite case; 19. Multiplication of negative partition relations for r = 2; 20. A negative partition relation established with the aid of GCH
21. Addition of negative partition relations for r =222. Addition of negative partition relations for r G 3; 23. Multiplication of negative partition relations in case r G 3; 24. The Negative Stepping-up Lemma; 25. Some special negative partition relations for r G 3; 26. The finite case of the ordinary partition relation; Chapter VI. The canonization lemmas; 27. Shelah's canonization; 28. The General Canonization Lemma; Chapter VII. Large cardinals; 29. The ordinary partition relation for inaccessible cardinals; 30. Weak compactness and a metamathematical approach to the Hanf-Tarski result
31. Baumgartner's principle32. A combinatorial approach to the Hanf-Tarski result; 33. Hanf's iteration scheme; 34. Saturated ideals, measurable cardinals. and strong partition relations; Chapter VIII. Discussion of the ordinary partition relation with superscript 2; 35. Discussion of the ordinary partition symbol in case r = 2; 36. Discussion of the ordinary partition relation in case r=2 under the assumption of GCH; 37. Sierpinski partitions; Chapter IX. Discussion of the ordinary partition relation with superscript G 3; 38. Reduction of the superscript
39. Applicability of the Reduction Theorem40. Consequences of the Reduction Theorem; 41. The main result for the case r G 3; 42. The main result for the case r G 3 with GCH; Chapter X. Some applications of combinatorial metbods; 43. Applications in topology; 44. Fodor's and Hajnal's set-mapping theorems; 45. Set mapping of type > 1; 46. Finite free sets with respect to set mappings of type > 1; 47. Inequalities for powers of singular cardinals; 48. Cardinal exponentiation and saturated ideals; Chapter XI. A brief survey of the square bracket relation
49. Negative square bracket relations and the GCH

Beteiligte: Erdös, Paul [Sonstige Person, Familie und Körperschaft]

Erschienen: Amsterdam; New York; New York, N.Y: North-Holland Pub. Co, 1984

Umfang: Online Ressource (347 pages)

Sprache: Englisch

ISBN: 1299773486; 9781299773486; 9780080961; 9789780080969; 0444861572; 9780444537454; 0444537457; 9780444861573

RVK-Notation: SK 170 : Kombinatorik (klassisch)
SK 150 : Mengenlehre und Verbandstheorie, allgemein

Schlagwörter: Partition > Kardinalzahl

Entstehung:

Anmerkungen: Includes indexes. - Includes bibliographical references (pages 335-340). - Print version record
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002

Beschreibung: This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel'skii's famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of recent inequalities for cardinal powers that were obtained in the wake of Silver's breakthrough result saying that the continuum hypothesis can not first fail at a singular cardinal of uncountable cofinality

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