Weak axioms of determinacy and subsystems of analysis. II \((\Sigma ^ 0_ 2\) games)

DOI10.1016/0168-0072(91)90045-NzbMath0729.03033OpenAlexW1979890335WikidataQ114684039 ScholiaQ114684039MaRDI QIDQ805613

Kazuyuki Tanaka

Publication date: 1991

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(91)90045-n

zbMATH Keywords

calibration subsystems of second-order arithmeticmonotone inductive definitionProof-theoretic strength of \(\Sigma ^ 0_ 2\)-determinacytwo-player infinite game

Mathematics Subject Classification ID

2-person games (91A05) Second- and higher-order arithmetic and fragments (03F35) Determinacy principles (03E60) Hierarchies of computability and definability (03D55)

Related Items (17)

Parallel Feedback Turing Computability ⋮ Reverse Mathematics: The Playground of Logic ⋮ Δ₃^O-determinacy, comprehension and induction ⋮ Determinacy and monotone inductive definitions ⋮ Determinacy in third order arithmetic ⋮ Open determinacy for class games ⋮ Locally hyperarithmetical induction ⋮ Lipschitz and Wadge binary games in second order arithmetic ⋮ Complete Determinacy and Subsystems of Second Order Arithmetic ⋮ The determinacy strength of \(\Pi_2^1\)-comprehension ⋮ Borel quasi-orderings in subsystems of second-order arithmetic ⋮ A characterization of \(\Sigma_1^1\)-reflecting ordinals ⋮ Weak systems of determinacy and arithmetical quasi-inductive definitions ⋮ Determinacy of Wadge classes and subsystems of second order arithmetic ⋮ CALIBRATING DETERMINACY STRENGTH IN LEVELS OF THE BOREL HIERARCHY ⋮ GAMES AND REFLECTION IN ⋮ Comparing inductive and circular definitions: Parameters, complexity and games

Cites Work

• Fixed point theory in weak second-order arithmetic
• The Galvin-Prikry theorem and set existence axioms
• Descriptive set theory
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