Partition Theorems and Ultrafilters
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Publication:4166748
DOI10.2307/1998845zbMath0386.03024OpenAlexW4256360806MaRDI QIDQ4166748
James E. Baumgartner, Alan D. Taylor
Publication date: 1978
Full work available at URL: https://doi.org/10.2307/1998845
Consistency and independence results (03E35) Large cardinals (03E55) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Other combinatorial set theory (03E05)
Related Items (27)
Combinatorics of open covers. VIII ⋮ Selctive ultrafilters and homogeneity ⋮ Selection principles and Sierpinski sets ⋮ Certain observations on selection principles from (a) Bornological viewpoint ⋮ Ultrafilters on \(\omega\) and atoms in the lattice of uniformities. I ⋮ Ultrafilters on \(\omega\) and atoms in the lattice of uniformities. II ⋮ Combinatorics of open covers. I: Ramsey theory ⋮ Ramsey type properties of ideals ⋮ Topological Ramsey spaces from Fraïssé classes, Ramsey-classification theorems, and initial structures in the Tukey types of \(p\)-points ⋮ In memoriam: James Earl Baumgartner (1943--2011) ⋮ Some further results on \(\mathcal I\)-\(\gamma\) and \(\mathcal I\)-\(\gamma_k\)-covers ⋮ Negative Partition Relations for Ultrafilters on Uncountable Cardinals ⋮ Scales, fields, and a problem of Hurewicz ⋮ Open covers and the square bracket partition relation ⋮ Large sets in Boolean and non-Boolean groups and topology ⋮ There is a Van Douwen MAD family ⋮ Applications of \(k\)-covers ⋮ Partition relations for Hurewicz-type selection hypotheses ⋮ Ramsey theory and the Borel conjecture ⋮ Forcing with filters and complete combinatorics ⋮ There are no P-points in Silver extensions ⋮ Superfilters, Ramsey theory, and van der Waerden's theorem ⋮ CLASSES OF BARREN EXTENSIONS ⋮ Ramsey degrees of ultrafilters, pseudointersection numbers, and the tools of topological Ramsey spaces ⋮ Hierarchies of measure-theoretic ultrafilters ⋮ Some covering properties in topological and uniform spaces ⋮ Some remarks on open covers and selection principles using ideals
Cites Work
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- Partitions of finite relational and set systems
- A new proof that analytic sets are Ramsey
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- Internal cohen extensions
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- Some applications of iterated ultrapowers in set theory
- Ultrafilters and Standard Functions in Non-Standard Arithmetic
- Ultrafilters over measurable cardinals
- Ultrafilters and Independent Sets
- On some problems of Hausdorff and of Sierpiński
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