Open AccessSelective ultrafilters and πβ(π)^{π}
Author(s) -
Todd Eisworth
Publication year - 1999
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-99-04835-2
Subject(s) - algorithm , annotation , artificial intelligence , type (biology) , computer science , mathematics , biology , ecology
Mathias ( Happy families , Ann. Math. Logic. 12 (1977), 59β111) proved that, assuming the existence of a Mahlo cardinal, it is consistent that CH holds and every set of reals in L ( R ) L(\mathbb {R}) is U \mathcal {U} -Ramsey with respect to every selective ultrafilter U \mathcal {U} . In this paper, we show that the large cardinal assumption cannot be weakened.