FOM: Re: GCH for some cardinal nos.

Jan Mycielski jmyciel at euclid.Colorado.EDU
Mon May 8 16:26:37 EDT 2000


	In my ANNOUNCEMENT of December 3, 1999 on f.o.m. an axiom called
LAD was inconsistent. A version which appears to be consistent in ZFC,
which still has all the consequences announced there, is the following.
	Let X be a subset of {0, 1}^alpha, where alpha is any regular
ordinal). Consider a game of perfect information where player I chooses
any ordinal beta_0 < alpha, and a sequence s_0 in {0, 1}^beta_0, then
player II chooses s_1 in {0, 1}, and again I chooses any beta_2 < alpha
and a sequence s_2 in {0, 1}^beta_2, and II choses s_3 in {0, 1}, etc. for
alpha steps. Notice that, since alpha is regular, the juxtaposition s =
s_0s_1s_2s_3... belongs to {0, 1}^alpha. Player I wins if s is in A, and
player II wins otherwise.
	The corrected version of LAD is: The above game is determined
whenever X belongs to OD.
						Jan Mycielski

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