Fundamental notions of analysis in subsystems of second-order arithmetic

Annals of Pure and Applied Logic 139 (1):138-184 (2006)
We develop fundamental aspects of the theory of metric, Hilbert, and Banach spaces in the context of subsystems of second-order arithmetic. In particular, we explore issues having to do with distances, closed subsets and subspaces, closures, bases, norms, and projections. We pay close attention to variations that arise when formalizing definitions and theorems, and study the relationships between them
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DOI 10.1016/j.apal.2005.03.004
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References found in this work BETA
Proof Mining in L1-Approximation.Ulrich Kohlenbach & Paulo Oliva - 2003 - Annals of Pure and Applied Logic 121 (1):1-38.
Vitali's Theorem and WWKL.Douglas K. Brown, Mariagnese Giusto & Stephen G. Simpson - 2002 - Archive for Mathematical Logic 41 (2):191-206.
Located Sets and Reverse Mathematics.Mariagnese Giusto & Stephen G. Simpson - 2000 - Journal of Symbolic Logic 65 (3):1451-1480.

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The Metamathematics of Ergodic Theory.Jeremy Avigad - 2009 - Annals of Pure and Applied Logic 157 (2):64-76.
Gödel Functional Interpretation and Weak Compactness.Ulrich Kohlenbach - 2012 - Annals of Pure and Applied Logic 163 (11):1560-1579.
Corrigendum To: 'A Constructive View on Ergodic Theorems'.Bas Spitters - 2006 - Journal of Symbolic Logic 71 (4):1431 - 1432.

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