A Non-Standard Construction of Haar Measure and Weak Konig's Lemma

Tanaka, Kazuyuki; Yamazaki, Takeshi

J. Symbolic Logic, Tome 65 (2000) no. 1, p. 173-186 / Harvested from Project Euclid

Résumé

In this paper, we show within $\mathbf{RCA_0}$ that weak Konig's lemma is necessary and sufficient to prove that any (separable) compact group has a Haar measure. Within $\mathbf{WKL_0}$, a Haar measure is constructed by a non-standard method based on a fact that every countable non-standard model of $\mathbf{WKL_0}$ has a proper initial part isomorphic to itself [10].

Publié le : 2000-03-14
Classification:

@article{1183746014,
     author = {Tanaka, Kazuyuki and Yamazaki, Takeshi},
     title = {A Non-Standard Construction of Haar Measure and Weak Konig's Lemma},
     journal = {J. Symbolic Logic},
     volume = {65},
     number = {1},
     year = {2000},
     pages = { 173-186},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746014}
}

Tanaka, Kazuyuki; Yamazaki, Takeshi. A Non-Standard Construction of Haar Measure and Weak Konig's Lemma. J. Symbolic Logic, Tome 65 (2000) no. 1, pp.  173-186. http://gdmltest.u-ga.fr/item/1183746014/