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