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

摘要

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