Tuesday, April 4 from 3 to 4pm

*Room*: MB 124

*Speaker*: Marion Scheepers (BSU)

*Title*: Playing an infinitely long game when you have limited memory (IV)

*Abstract*: We consider a class of infinite games in which player TWO has a winning strategy (based on perfect memory). In prior talks in this series we considered the effect of a limited memory where TWO remembers only the most recent move of ONE and of TWO, or TWO remembers a limited number of prior moves of ONE only.

As in these prior talks we consider the game where ONE chooses a first category subset of a space, and TWO chooses a nowhere dense set each inning. ONE’s sets are strictly increasing from inning to inning. For a fixed k, TWO remembers only the most recent k moves of ONE. We discussed why for k=1 only in the simplest of circumstances TWO has a winning 1-tactic. We also outline how in certain examples TWO had a winning 2-tactic ($k=2$). In this talk we will focus on the case when TWO does not have a winning 2-tactic, but does have a winning k-tactic for some $k>2$.