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

Published online by Cambridge University Press:  12 March 2014

Kazuyuki Tanaka  and
Takeshi Yamazaki
Kazuyuki Tanaka
Affiliation:
Mathematical Institute, Tohoku University, Sendai 980-8578Japan
Takeshi Yamazaki
Affiliation:
Mathematical Institute, Tohoku University, Sendai 980-8578Japan
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Abstract

In this paper, we show within RCA0 that weak König's lemma is necessary and sufficient to prove that any (separable) compact group has a Haar measure. Within WKL0, a Haar measure is constructed by a non-standard method based on a fact that every countable non-standard model of WKL0 has a proper initial part isomorphic to itself [10].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 1 , March 2000 , pp. 173 - 186
Copyright
Copyright © Association for Symbolic Logic 2000

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References

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