Geodesic
The Saturation of a Product of Ideals
Canadian journal of mathematics, Tome 32 (1980) no. 1, pp. 70-75

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we discuss how the saturation I X J, where I, J are k-complete ideals on a regular uncountable cardinal K, depends on the saturation of I and J. We show that if 2k = k+ then the saturation of I X J is completely determined by the saturation of I and J . A consequence of a negative saturation result is that NSk X NSk is not k+-saturated, where NSk is the nonstationary ideal on k (even though it is still open whether NSk can be K+- saturated). We also discuss the preservation of precipitousness under certain products, obtaining a simple example of an ideal on kthat is precipitous but not k+-saturated. 
Wagon, Stanley. The Saturation of a Product of Ideals. Canadian journal of mathematics, Tome 32 (1980) no. 1, pp. 70-75. doi: 10.4153/CJM-1980-007-9
@article{10_4153_CJM_1980_007_9,
     author = {Wagon, Stanley},
     title = {The {Saturation} of a {Product} of {Ideals}},
     journal = {Canadian journal of mathematics},
     pages = {70--75},
     year = {1980},
     volume = {32},
     number = {1},
     doi = {10.4153/CJM-1980-007-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-007-9/}
}
TY  - JOUR
AU  - Wagon, Stanley
TI  - The Saturation of a Product of Ideals
JO  - Canadian journal of mathematics
PY  - 1980
SP  - 70
EP  - 75
VL  - 32
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-007-9/
DO  - 10.4153/CJM-1980-007-9
ID  - 10_4153_CJM_1980_007_9
ER  - 
%0 Journal Article
%A Wagon, Stanley
%T The Saturation of a Product of Ideals
%J Canadian journal of mathematics
%D 1980
%P 70-75
%V 32
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1980-007-9/
%R 10.4153/CJM-1980-007-9
%F 10_4153_CJM_1980_007_9

[1] 1. Jech, T., Magidor, M., Mitchell, W. and Prikry, K., Precipitous ideals, J. Sym. Logic (to appear). Google Scholar

[2] 2. Jech, T. and Prikry, K., Ideals over uncountable sets: application of almost disjoint functions and generic ultrapowers, Memoirs A.M.S. 214 (1979). Google Scholar

[3] 3. Kakuda, Y., Saturated ideals in Boolean extensions, Nagoya Math. J. 48 (1972), 159–168. Google Scholar

[4] 4. Prikry, K. L., Changing measurable into accessible cardinals, Dissertationes Math. 68 (1970). Google Scholar

[5] 5. Solovay, R. M., Real-valued measurable cardinals, in Axiomatic Set Theory, Proc. Symp. Pure Math. 13 (1) (1971), 397–428. Google Scholar

[6] 6. Tarski, A., Idéale in vollstdndigen Mengenkorpern II, Fund. Math. 13 (1945), 51–65. Google Scholar

[7] 7. Taylor, A., Regularity properties of ideals and ultrafilters, Ann. Math. Logi. 16 (1979), 33–55. Google Scholar

[8] 8. Ulam, S., Zur Masstheorie in der Allgemeinen Mengenlehre, Fund. Math. 16 (1930), 140–150. Google Scholar

[9] 9. Wagon, S., Decompositions of saturated ideals, Ph.D. Thesis, Dartmouth College (1975). Google Scholar

Cité par Sources :