We investigate Martin's game (as described in Arruda et al. (Eds.), On Random R. E. Sets, Non-Classical Logics, Model Theory and Computability, North-Holland, Amsterdam, 1977, p. 283) and prove that the upper bound from the above mentioned reference for the number of sets needed to construct a winning strategy, is almost tight. c 2002 Elsevier Science B.V. All rights reserved.
M. Ageev