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Reverse mathematics of separably closed sets

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Abstract

This paper contains a corrected proof that the statement “every non-empty closed subset of a compact complete separable metric space is separably closed” implies the arithmetical comprehension axiom of reverse mathematics.

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References

  1. Brown, D. K.: Functional analysis in weak subsystems of second order arithmetic. PhD thesis, The Pennsylvania State University, 1987

  2. Brown, D. K.: Notions of closed subsets of a complete separable metric space in weak subsystems of second order arithmetic. In: Sieg, W. (ed.), Logic and computation (Pittsburgh, PA, 1987), volume 106 of Contemporary Mathematics, pages 39–50. Providence, RI: Amer. Math. Soc., 1990

  3. Hirst, J. L.: Minima of initial segments of infinite sequences of reals. Mathematical Logic Quarterly, 50, 47–50 (2004)

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  4. Simpson, S. G.: Subsystems of second order arithmetic. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1999

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Hirst, J. Reverse mathematics of separably closed sets. Arch. Math. Logic 45, 1–2 (2006). https://doi.org/10.1007/s00153-005-0298-7

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  • DOI: https://doi.org/10.1007/s00153-005-0298-7

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