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Author:   William Wistar Comfort ,  S. Negrepontis
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Volume:   211
Weight:   0.900kg
ISBN:  

9783540066040

ISBN 10:   3540066047
Pages:   494
Publication Date:   05 November 1974
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Out of Print
Availability:   Out of stock  

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 Jonsson Classes.- Notes for 4.- 5. The Jonsson Class of Ordered Sets.- Notes for 5.- 6. The Jonsson 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's Characterisation 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 ?:?(? x ?) ? ?(?) x ?(?).- The Rudin-Frolik Order.- Non-Homogeneity of Certain Spaces.- Notes for 16.- Index of Symbols.

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