A non-standard construction of Haar measure and weak könig's lemma

Journal of Symbolic Logic 65 (1):173-186 (2000)
In this paper, we show within RCA 0 that weak Konig's lemma is necessary and sufficient to prove that any (separable) compact group has a Haar measure. Within WKL 0 , a Haar measure is constructed by a non-standard method based on a fact that every countable non-standard model of WKL 0 has a proper initial part isomorphic to itself [10]
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DOI 10.2307/2586530
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Kazuyuki Tanaka (1997). Non‐Standard Analysis in WKL0. Mathematical Logic Quarterly 43 (3):396-400.

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