This is a followup to a paper by the author where the disjointness relation
for definable functions from ΟΟ to ΟΟ is
analyzed. In that paper, for each aβΟΟ we defined a Baire
class one function faβ:ΟΟβΟΟ which encoded
a in a certain sense. Given g:ΟΟβΟΟ, let
Ξ¨(g) be the statement that g is disjoint from at most countably many of
the functions faβ. We show the consistency strength of (βg)Ξ¨(g) is that of an inaccessible cardinal. We show that AD+
implies (βg)Ξ¨(g). Finally, we show that assuming large
cardinals, (βg)Ξ¨(g) holds in models of the form
L(R)[U] where U is a selective ultrafilter on
Ο.Comment: 16 page