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Author:   W.W. Comfort ,  S. Negrepontis
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1974
Volume:   211
Dimensions:   Width: 15.20cm , Height: 2.50cm , Length: 22.90cm
Weight:   0.726kg
ISBN:  

9783642657825

ISBN 10:   3642657826
Pages:   484
Publication Date:   12 November 2011
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

§1. Set Theory.- Ordinals.- Cardinal Arithmetic.- Notes for §1.- § 2. Topology and Boolean Algebras.- Topology.- Finitary Properties of Boolean Algebras.- Stone’s Duality.- The Completion of a Boolean Algebra and the Gleason Space of a Compact Space.- Notes for §2.- §3. Intersection Systems and Families of Large Oscillation.- Intersection Systems and the Souslin Number.- Families of Large Oscillation.- Notes for §3.- § 4. The General Theory of Jönsson Classes.- Notes for §4.- §5. The Jónsson Class of Ordered Sets.- Notes for §5.- § 6. The Jónsson Class of Boolean Algebras.- The Stone Space of the Homogeneous-Universal Boolean Algebras.- Properties of the Space S?.- Notes for §6.- § 7. Basic Facts on Ultrafilters.- Notes for §7.- §8. Large Cardinals.- Weakly Compact Cardinals: Combinatorial Equivalences.- Weakly Compact Cardinals: Boolean-Algebraic and Topological Equivalences.- Measurable Cardinals.- Descendingly Incomplete Ultrafilters.- Notes for §8.- § 9. The Rudin-Keisler Order on Types of Ultrafilters.- The Rudin-Keisler Order.- Rudin-Keisler Minimal Types in ?[?(?)\?].- Good Ultrafilters.- Notes for §9..- § 10. Good Ultrafilters.- Families of Large Oscillation Modulo Filters; the Fundamental Existence Theorem of Good Ultrafilters.- Additional Existence Results.- Directedness Properties of the Rudin-Keisler Order.- Adequate Ultrafilters on Special Boolean Algebras.- Notes for §10.- § 11. Elementary Types.- Notes for §11.- § 12. Families of Almost Disjoint Sets.- Cardinalities of Families of Almost Disjoint Sets.- The Balcar-Vop?nka Theorem.- Cardinalities of Ultraproducts.- Notes for § 12.- §13. Saturation of Ultraproducts.- Ultraproducts Modulo Regular Ultrafilters.- Ultraproducts Modulo Good Ultrafilters.- Shelah’sCharacterisation of Elementary Equivalence.- Characterisation of the Rudin-Keisler Order.- Notes for §13.- § 14. Topology of Spaces of Ultrafilters.- Certain Properties of F?-Spaces.- The Space of ?-Uniform Ultrafilters on ?.- Spaces of Uniform Ultrafilters and Homogeneous-Universal Boolean Algebras.- The Space of Sub-Uniform Ultrafilters.- Relations to Measurable Cardinals.- Notes for §14.- §15. Spaces Homeomorphic to (2?)?.- The Topological Characterization of (2?)?.- The Baire Category Properties of (2?)?.- Spaces of Ultrafilters Homeomorphic to Spaces (2?)?.- Applications to the Growth Spaces ?X\X.- Notes for §15.- § 16. Ultrafilters on ?.- The Rudin-Keisler Order on ?(?) and the Canonical Function ?:?(? × ?) ? ?(?) × ?(?).- The Rudin-Frolík Order.- Non-Homogeneity of Certain Spaces.- Notes for §16.- Index of Symbols.

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