ML-1994-13: An Elementary Construction of an Ultrafilter on $\aleph_1$ Using the Axiom of Determinateness

ML-1994-13: Vervoort, Marco R. (1994) An Elementary Construction of an Ultrafilter on $\aleph_1$ Using the Axiom of Determinateness. [Report]

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Abstract

An elementary construction of an ultrafilter on Aleph­One
using the Axiom of Determinateness
Marco R. Vervoort

In this article we construct a free and s­complete ultrafilter on the set
\omega_1, using AD.
First we define for each V \subset \omega_1 a game G(V). From the axiom
AD we have that for each V \subset \omega_1 , either the first or the
second player has a winning strategy in G(V). We then show, in several
lemma's, how to obtain winning strategies in G(V) for several different
constructions of V from other sets. Finally, we show that the collection
{ V \subset \omega_1 | the first player has a winning strategy in G(V) }
has several closure properties corresponding to the lemma's just proved,
and that this set is in fact a free and \sigma­complete ultrafilter.

Item Type:	Report
Report Nr:	ML-1994-13
Series Name:	Mathematical Logic and Foundations (ML)
Year:	1994
Date Deposited:	12 Oct 2016 14:40
Last Modified:	24 Jun 2022 00:06
URI:	https://eprints.illc.uva.nl/id/eprint/1359

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