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\begin{flushright}
  A. Miller \\
  M873        \\
  Topics in Descriptive Set Theory \\
  Fall 2000 \\
\end{flushright}

\topic Open games are determined (Gale-Stewart \cite{gs}).
\topic $G_\delta$ games are determined (Wolfe \cite{wolfe})
\topic P implies $\omega_1$ is inaccessible in L (Levy \cite{levy})
\topic AD implies P, every set of reals is countable or contains a perfect subset
 (Davis \cite{davis})
\topic Inconsistent versions of AD (Mycielski \cite{myc})
\topic DC iff Baire category theorem (Blair \cite{blair}, Goldblatt
 \cite{gold})
\topic (ZFC) $L[\R]\models$``ZF+DC'' (Takeuti \cite{tak})
\topic Equivalence of AD$_\R$ and AD for games of length $\omega^2$
 (Blass \cite{blass})
\topic Banach-Mazur games and Baire property, AD implies BP (see Oxtoby
 \cite{oxtoby})
\topic AD$_\R$ implies every set $A\subseteq [\omega]^\omega$ is
completely Ramsey (Prikry \cite{prikry} also Ellentuck \cite{ellen})
\topic AD for Banach games is equivalent to AD (Freiling \cite{freiling},
Becker \cite{becker})
\topic AD implies LM, every set is Lebesgue measurable
(Mycielski,Swierczkowski \cite{myciel})
\topic The boundedness theorem for ${\bf \Pi}^1_1$
\topic AD implies the club filter on $\omega_1$ is an ultrafilter,
(Solovay 1967, see Kechris \cite{kecp})
\topic Wadge's Lemma, well-foundedness of Wadge ordering,
(Wadge, Martin, Monk, see Van Wesep \cite{vanwesep})
\topic PWO($\Gamma$) implies Red($\Gamma$) implies Sep(dual$\Gamma$)
and not Sep($\Gamma$)
\topic PWO(${\bf\Pi^1_1}$), PWO(${\bf\Sigma^1_2}$)
\topic (V=L) PWO(${\bf\Sigma^1_{n}}$) for $n\geq 2$
(Addison \cite{addison},\cite{addison2} see also \cite{mos})
\topic Projective Determanacy PD implies PWO(${\bf\Sigma^1_{n}}$)
for $n$ even and PWO(${\bf\Pi^1_{n}}$) for $n$ odd,
(Blackwell, Martin, Addison, Moschovakis see \cite{addison3}, \cite{mos})
\topic The Separation holds on exactly one side of a nonselfdual
Wadge class, (Steel \cite{steel}, Van Wesep \cite{van2})
\topic Borel sets are determined, (Martin \cite{martin1},\cite{martin2})
\topic Existence of measurable cardinal equivalent to an elementary
embedding (Los).  Measurable implies $V\not=L$ (Scott).
\topic Existence of measurables does not decide continuum hypothesis
(Levy, Solovay). No nontrival embedding of $V$ into $V$ (Kunen).
\topic Measurables are Ramsey, limit of Ramsey's (Rowbottom).  Erdos
cardinals are strongly inaccessible.
\topic Analytic sets are determined assuming there is a measurable
cardinal (or even Erdos cardinal), (Martin \cite{martin3})
\topic The theory of $0^\sharp$, Club of indiscernibles for $L$,
$\Pi^1_2$-singleton (Silver, Solovay, Rowbottom).
\topic Existence of $0^\sharp$ equivalent to a nontrivial elementary
embedding of $L$ into $L$ (Kunen).
\topic Sharps are equivalent to Analytic Determanacy, (Harrington \cite{har}
see also Sami \cite{sami})
\topic Equivalence of sharps, Wadge's lemma for $\Pi^1_1$, Borel isomorphism,
and $<\omega^2-\Pi^1_1$-det (Harrington, Steel, Martin, see
also Dubose \cite{dubose})


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\bibitem{addison2}
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\bibitem{addison3}
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\bibitem{becker}
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\bibitem{blair}
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\bibitem{freiling}
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Banach games.
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\bibitem{gs}
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\bibitem{har}
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\bibitem{kecp}
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\bibitem{levy}
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\bibitem{martin3}
Martin, Donald A.,
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\bibitem{martin1}
Martin, Donald A.,
Borel determinacy.
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\bibitem{martin2}
Martin, Donald A.,
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\bibitem{mos}
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Elsevier-North Holland, 1980.

\bibitem{myc}
Mycielski, Jan,
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Fund. Math. 53 1963/1964 205--224.


\bibitem{myciel}
Mycielski, Jan; \'Swierczkowski, S.,
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Fund. Math. 54 1964 67--71.

\bibitem{oxtoby}
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\bibitem{prikry}
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Determinateness and partitions.
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\bibitem{sami}
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\bibitem{steel}
Steel, John R.,
Determinateness and the separation property.
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\bibitem{tak}
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\bibitem{vanwesep}
Van Wesep, Robert,
Wadge degrees and descriptive set theory.
Cabal Seminar 76--77 (Proc. Caltech-UCLA Logic Sem., 1976--77), pp. 151--170,
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\bibitem{van2}
Van Wesep, Robert A.,
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J. Symbolic Logic 43 (1978), no. 1, 77--81.

\bibitem{wolfe}
Wolfe, Philip,
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\end{thebibliography}
\end{document}