Author | Comfort, W. Wistar. author |
---|---|
Title | The Theory of Ultrafilters [electronic resource] / by W. Wistar Comfort, Stylianos Negrepontis |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1974 |
Connect to | http://dx.doi.org/10.1007/978-3-642-65780-1 |
Descript | X, 484 p. online resource |
ยง1. Set Theory -- Ordinals -- Cardinal Arithmetic -- Notes for ยง1 -- ยง 2. Topology and Boolean Algebras -- Topology -- Finitary Properties of Boolean Algebras -- Stoneโs Duality -- The Completion of a Boolean Algebra and the Gleason Space of a Compact Space -- Notes for ยง2 -- ยง3. Intersection Systems and Families of Large Oscillation -- Intersection Systems and the Souslin Number -- Families of Large Oscillation -- Notes for ยง3 -- ยง 4. The General Theory of Jรถnsson Classes -- Notes for ยง4 -- ยง5. The Jรณnsson Class of Ordered Sets -- Notes for ยง5 -- ยง 6. The Jรณnsson Class of Boolean Algebras -- The Stone Space of the Homogeneous-Universal Boolean Algebras -- Properties of the Space S? -- Notes for ยง6 -- ยง 7. Basic Facts on Ultrafilters -- Notes for ยง7 -- ยง8. Large Cardinals -- Weakly Compact Cardinals: Combinatorial Equivalences -- Weakly Compact Cardinals: Boolean-Algebraic and Topological Equivalences -- Measurable Cardinals -- Descendingly Incomplete Ultrafilters -- Notes for ยง8 -- ยง 9. The Rudin-Keisler Order on Types of Ultrafilters -- The Rudin-Keisler Order -- Rudin-Keisler Minimal Types in ?[?(?)\?] -- Good Ultrafilters -- Notes for ยง9. -- ยง 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 ยง10 -- ยง 11. Elementary Types -- Notes for ยง11 -- ยง 12. Families of Almost Disjoint Sets -- Cardinalities of Families of Almost Disjoint Sets -- The Balcar-Vop?nka Theorem -- Cardinalities of Ultraproducts -- Notes for ยง 12 -- ยง13. Saturation of Ultraproducts -- Ultraproducts Modulo Regular Ultrafilters -- Ultraproducts Modulo Good Ultrafilters -- Shelahโs Characterisation of Elementary Equivalence -- Characterisation of the Rudin-Keisler Order -- Notes for ยง13 -- ยง 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 ยง14 -- ยง15. 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 ยง15 -- ยง 16. Ultrafilters on ? -- The Rudin-Keisler Order on ?(?) and the Canonical Function ?:?(? ร ?) ? ?(?) ร ?(?) -- The Rudin-Frolรญk Order -- Non-Homogeneity of Certain Spaces -- Notes for ยง16 -- Index of Symbols