Previous |  Up |  Next


category base; precipitous ideal; measurable cardinal
We show that the existence of a non-trivial category base on a set of regular cardinality with each subset being Baire is equiconsistent to the existence of a measurable cardinal.
[J] Jech T.: Set Theory. Academic Press, 1978. MR 0506523 | Zbl 1007.03002
[JP] Jech T., Magidor M., Mitchell W., Prikry K.: Precipitous ideals. Journal of Symbolic Logic 45 1-8. MR 0560220 | Zbl 0437.03026
[KT] Kunen K., Szymański A., Tall F.: Baire irresolvable spaces and ideal theory. Acta Math. Silesiana, No. 14 (1986), 98-107. MR 0861505
[M1] Morgan J.C.II: Point Set Theory. Marcel Dekker, Inc., 1990. MR 1026014 | Zbl 0937.26519
[S] Solovay R.: Real valued measurable cardinals. in Axiomatic Set Theory, Proc. Symp. Pure Math. 13.1 (D. Scott ed.), 397-428, Amer. Math. Soc., 1971. MR 0290961 | Zbl 0222.02078
Partner of
EuDML logo