A notion of selective ultrafilter corresponding to topological Ramsey spaces

DOI10.1002/MALQ.200510045zbMath1126.03044arXivmath/0510517OpenAlexW2041290640MaRDI QIDQ5293196

José G. Mijares

Publication date: 26 June 2007

Published in: Mathematical Logic Quarterly (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510517

zbMATH Keywords

forcingopen coloring axiomRamsey ultrafilterultrafilterRamsey's theoremRamsey spaceMathias forcingSolovay modelEllentuck space

Mathematics Subject Classification ID

Inner models, including constructibility, ordinal definability, and core models (03E45) Other combinatorial set theory (03E05) Partition relations (03E02) Other aspects of forcing and Boolean-valued models (03E40)

Related Items (16)

The space of infinite partitions of $\mathbb{N}$ as a topological Ramsey space ⋮ Topological Ramsey spaces from Fraïssé classes, Ramsey-classification theorems, and initial structures in the Tukey types of \(p\)-points ⋮ On Galvin's lemma and Ramsey spaces ⋮ Ramsey for R1 ultrafilter mappings and their Dedekind cuts ⋮ Filters on a countable vector space ⋮ A canonical partition theorem for uniform families of finite strong subtrees ⋮ Selective ultrafilters on FIN ⋮ Local Ramsey theory: an abstract approach ⋮ Preserved under Sacks forcing again? ⋮ Topological Ramsey spaces and metrically Baire sets ⋮ A new class of Ramsey-classification theorems and their application in the Tukey theory of ultrafilters, Part 1 ⋮ A local Ramsey theory for block sequences ⋮ CLASSES OF BARREN EXTENSIONS ⋮ A new class of Ramsey-classification theorems and their applications in the Tukey theory of ultrafilters, Part 2 ⋮ Ramsey degrees of ultrafilters, pseudointersection numbers, and the tools of topological Ramsey spaces ⋮ Selective but not Ramsey

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