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Zoekopdracht: faculteit: "FNWI" en publicatiejaar: "1997"

AuteurBrian Semmes
TitelThe Raisonnier-Shelah Construction of a Non-Measurable Set
FaculteitFaculteit der Natuurwetenschappen, Wiskunde en Informatica
Instituut/afd.FNWI/FGw: Institute for Logic, Language and Computation (ILLC)
SerieILLC Master of Logic Theses / ILLC ; MoL-1997-02
SamenvattingThe Raisonnier�Shelah construction of a non�measurable set
Brian Semmes

In this paper 1 we will give a proof of the following theorem of S. Shelah.

Theorem 1:
In Zermelo Fraenkel set theory (ZF) plus the axiom of dependent choice (DC),
we can prove that there is a non�measurable set if there is an uncountable
well�ordered set of reals.

Shelah's proof uses rather sophisticated meta�mathematical arguments that
may not be accessible to the general mathematician. As our principle goal
is to reach a relatively wide audience, we will use the ideas of J. Raisonnier,
who has given a simpler and less meta�mathematical proof of Theorem 1. However
we will not follow Raisonnier's proof exactly. We will make some
simplifications to Raisonnier's arguments and we will also follow to a certain
extent the exposition of Raisonnier's proof presented in M. Bekkali's lecture
notes for a seminar taught by S. Todorcevic.
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