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A non-standard construction of Haar measure and weak könig's lemma
Journal of Symbolic Logic 65 (1):173-186 (2000)
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]Links
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Citations of this work
The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic.Nobuyuki Sakamoto & Keita Yokoyama - 2007 - Archive for Mathematical Logic 46 (5-6):465-480.
Nonstandard second-order arithmetic and Riemannʼs mapping theorem.Yoshihiro Horihata & Keita Yokoyama - 2014 - Annals of Pure and Applied Logic 165 (2):520-551.
Tanaka’s theorem revisited.Saeideh Bahrami - 2020 - Archive for Mathematical Logic 59 (7-8):865-877.
References found in this work
Which set existence axioms are needed to prove the separable Hahn-Banach theorem?Douglas K. Brown & Stephen G. Simpson - 1986 - Annals of Pure and Applied Logic 31:123-144.
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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