The Galvin-Prikry theorem and set existence axioms

DOI10.1016/0168-0072(89)90066-3zbMath0667.03043OpenAlexW2136623171WikidataQ114684041 ScholiaQ114684041MaRDI QIDQ1117221

Kazuyuki Tanaka

Publication date: 1989

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(89)90066-3

zbMATH Keywords

Reverse Mathematicsformal provability in weak universal systems

Mathematics Subject Classification ID

Second- and higher-order arithmetic and fragments (03F35)

Related Items (7)

Parallel Feedback Turing Computability ⋮ Reverse mathematics and initial intervals ⋮ Well ordering principles for iterated \(\Pi^1_1\)-comprehension ⋮ Fraïssé’s conjecture in Π11-comprehension ⋮ Borel quasi-orderings in subsystems of second-order arithmetic ⋮ \({\Pi^1_2}\)-comprehension and the property of Ramsey ⋮ Weak axioms of determinacy and subsystems of analysis. II \((\Sigma ^ 0_ 2\) games)

Cites Work

• Addendum to ``Countable algebra and set existence axioms
• Descriptive set theory
• On the Ramsey property for sets of reals
• On the role of Ramsey quantifiers in first order arithmetic
• A new proof that analytic sets are Ramsey
• Uncountable Gandy Ordinals
• Happy families
• Sets which do not have subsets of every higher degree
• Hyperarithmetically Encodable Sets
• Borel sets and Ramsey's theorem
• A survey of proof theory
• Bar Induction and Π₁¹-CA
• Every analytic set is Ramsey
• Ramsey's theorem and recursion theory
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