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Measure theory and weak König's lemma

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Abstract

We develop measure theory in the context of subsystems of second order arithmetic with restricted induction. We introduce a combinatorial principleWWKL (weak-weak König's lemma) and prove that it is strictly weaker thanWKL (weak König's lemma). We show thatWWKL is equivalent to a formal version of the statement that Lebesgue measure is countably additive on open sets. We also show thatWWKL is equivalent to a formal version of the statement that any Borel measure on a compact metric space is countably additive on open sets.

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Authors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, Altoona Campus, 16601, Altoona, PA, USA

    Xiaokang Yu

  2. Department of Mathematics, Pennsylvania State University, 16802, University Park, PA, USA

    Stephen G. Simpson

Authors
  1. Xiaokang Yu
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  2. Stephen G. Simpson
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The research of both authors was partially supported by NSF Grant DMS-8701481.

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Yu, X., Simpson, S.G. Measure theory and weak König's lemma. Arch Math Logic 30, 171–180 (1990). https://doi.org/10.1007/BF01621469

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  • DOI: https://doi.org/10.1007/BF01621469

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