TY - JOUR
T1 - Q-sets, sierpinski sets, and rapid filters
AU - Judah, Haim
AU - Shelah, Saharon
PY - 1991/3
Y1 - 1991/3
N2 - In this work we will prove the following:Theorem 1. cons(ZF) implies cons(Z.FC+ there exists a Q-set of reals + there exists a set of reals of cardinality N, which is not Lebesgue measurable). Theorem 2. cons(ZF) implies cons(ZFC + 20is arbitrarily larger than H2+ there exists a Sierpinski set of cardinality 20) +there are no rapid filters on a). These theorems give answers to questions of Fleissner[Fl] and Judah [Ju].
AB - In this work we will prove the following:Theorem 1. cons(ZF) implies cons(Z.FC+ there exists a Q-set of reals + there exists a set of reals of cardinality N, which is not Lebesgue measurable). Theorem 2. cons(ZF) implies cons(ZFC + 20is arbitrarily larger than H2+ there exists a Sierpinski set of cardinality 20) +there are no rapid filters on a). These theorems give answers to questions of Fleissner[Fl] and Judah [Ju].
UR - http://www.scopus.com/inward/record.url?scp=84968510056&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-1991-1045594-5
DO - 10.1090/S0002-9939-1991-1045594-5
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AN - SCOPUS:84968510056
SN - 0002-9939
VL - 111
SP - 821
EP - 832
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 3
ER -