English

Meager-nowhere dense games (III): Remainder strategies

Logic 2009-09-25 v1

Abstract

Player ONE chooses a meager set and player TWO, a nowhere dense set per inning. They play ω\omega many innings. ONE's consecutive choices must form a (weakly) increasing sequence. TWO wins if the union of the chosen nowhere dense sets covers the union of the chosen meager sets. A strategy for TWO which depends on knowing only the uncovered part of the most recently chosen meager set is said to be a remainder strategy. Theorem (among others): TWO has a winning remainder strategy for this game played on the real line with its usual topology.

Keywords

Cite

@article{arxiv.math/9209208,
  title  = {Meager-nowhere dense games (III): Remainder strategies},
  author = {Marion Scheepers},
  journal= {arXiv preprint arXiv:math/9209208},
  year   = {2009}
}