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

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Journal of Symbolic Logic 65 (1):173-186 (2000)
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Abstract

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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10.2307/2586530

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Citations of this work

Tanaka’s theorem revisited.Saeideh Bahrami - 2020 - Archive for Mathematical Logic 59 (7-8):865-877.

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References found in this work

Subsystems of Second Order Arithmetic.Stephen G. Simpson - 1999 - Studia Logica 77 (1):129-129.
Measure theory and weak König's lemma.Xiaokang Yu & Stephen G. Simpson - 1990 - Archive for Mathematical Logic 30 (3):171-180.
Fixed point theory in weak second-order arithmetic.Naoki Shioji & Kazuyuki Tanaka - 1990 - Annals of Pure and Applied Logic 47 (2):167-188.

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