Preprint No.
A-02-05
Stefan Geschke
Analytic determinacy and #'s
Abstract:
Martin showed that all Borel games are
determined. However, this cannot be extended in ZFC. In this article we
show that already the determinacy of analytic games implies the existence of
large cardinals. More precisely, we present a proof of the following theorem:
Analytic determinacy implies the existence of
$x^\sharp$ for all $x\subseteq\omega$.
This theorem is an initial segment of the
famous Martin-Steel Theorem that established a deep connection
between the existence of certain large cardinals and the determinacy of
certain classes of sets of reals.
Like in Harrington's original paper we will only show the theorem for
$0^\sharp$ since the proof relativizes to every $x\subseteq\omega$
giving the existence of $x^\sharp$.
Keywords:
determinacy, analytic games, sharps,
large cardinals
Mathematics Subject Classification (MSC2000):
Primary: 03E60, 03E55; Secondary: 03E15
Language: ENG
Available: Pr-A-02-05.ps
Contact: Stefan Geschke, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (geschke@math.fu-berlin.de)
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