Games in logic
Most of the games studied in this Colloquium have appeared in logic at
some time. Happily I can leave proof-theoretic games to Krabbe, and
forcing games to Hirsch and Hodkinson. This leaves three main types:
(1) semantic games, which include quantifier games and the
Barwise-Etchemendy teaching game 'Tarski's World'; (2) comparison
games such as back-and-forth and bisimulation; (3) cut-and-choose
games, including various model-theoretic rank operations and
Vapnik-Chervonenkis dimension from learning theory. These games all
have a common theme: the number of steps for which the second player
can stay alive is a useful measure of something meaningful.
Wilfrid Hodges