Fixed point theory in weak second-order arithmetic

DOI10.1016/0168-0072(90)90068-DzbMath0711.03026OpenAlexW2013342737MaRDI QIDQ922541

Naoki Shioji, Kazuyuki Tanaka

Publication date: 1990

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(90)90068-d

zbMATH Keywords

fixed pointsHahn-Banach theoremaffine mappings\(RCA_ 0\)\(WKL_ 0\)Brouwer's theoremCauchy- Peano theorem for ordinary differential equationsinfinite dimensional analogueMarkov-Kukutani theoremweak subsystems of second-order arithmetic

Mathematics Subject Classification ID

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

Related Items (16)

Separation and Weak König's Lemma ⋮ 2000 Annual Meeting of the Association for Symbolic Logic ⋮ The Brouwer Fixed Point Theorem Revisited ⋮ Complex analysis in subsystems of second order arithmetic ⋮ The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic ⋮ Primitive recursive reverse mathematics ⋮ Brouwer's fan theorem as an axiom and as a contrast to Kleene's alternative ⋮ Mixed Nash equilibria for continuous games and reverse mathematics ⋮ Two kinds of fixed point theorems and reverse mathematics ⋮ The Brouwer invariance theorems in reverse mathematics ⋮ Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation ⋮ Reverse mathematics and order theoretic fixed point theorems ⋮ How Incomputable is the Separable Hahn-Banach Theorem? ⋮ A non-standard construction of Haar measure and weak König's lemma ⋮ Connected choice and the Brouwer fixed point theorem ⋮ Weak axioms of determinacy and subsystems of analysis. II \((\Sigma ^ 0_ 2\) games)

Cites Work

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• A generalization of Tychonoff's fixed point theorem
• Countable algebra and set existence axioms
• Which set existence axioms are needed to prove the separable Hahn-Banach theorem?
• A generalization of the Hahn-Banach theorem
• Which set existence axioms are needed to prove the Cauchy/Peano theorem for ordinary differential equations?
• The Game of Hex and the Brouwer Fixed-Point Theorem

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