Itay Neeman
Backcover text:
In this volume the author develops and applies methods for proving,
from large cardinals, the determinacy of definable games of countable
length on natural numbers. The determinacy is ultimately
derived
from iteration strategies, connecting games on natural numbers
with
the specific iteration games that come up in the study of large
cardinals.
The games
considered in this text range in strength, from games of
fixed
countable length, through games where the length is clocked
by natural
numbers, to games in which a run is complete when its
length is
uncountable in an inner model (or a pointclass) relative to
the run.
More can be done using the methods developed here,
reaching
determinacy for games of length $\omega_1$.
The book
is largely self-contained. Only graduate level knowledge
of modern
techniques in large cardinals and basic forcing is assumed.
Several
exercises allow the reader to build on the results in the text,
for
example connecting them with universally Baire and
homogeneously
Suslin sets. Overall it is intended that the book
should be
accessible both to specialists and to advanced graduate
students in set theory