Skip to main content Accessibility help

Some pathological examples of precipitous ideals

  • Moti Gitik (a1)


We construct a model with an indecisive precipitous ideal and a model with a precipitous ideal with a non precipitous normal ideal below it. Such kind of examples were previously given by M. Foreman [2] and R. Laver [4] respectively. The present examples differ in two ways: first- they use only a measurable cardinal and second- the ideals are over a cardinal. Also a precipitous ideal without a normal ideal below it is constructed. It is shown in addition that if there is a precipitous ideal over a cardinal κ such that

• after the forcing with its positive sets the cardinality of κ remains above ℵ1

• there is no a normal precipitous ideal then there is 0.



Hide All
[1]Foreman, M., Ideals and generic elementary embeddings, Handbook of set theory, to appear.
[2]Foreman, M., Smoke and mirrors: combinatorial properties of small cardinals equiconsistent with huge cardinals, to appear.
[3]Gitik, M., On generic elementary embeddings, this Journal, vol. 54 (1989), no. 3, pp. 700707.
[4]Laver, R., Precipitousness in forcing extensions, Israel Journal of Mathematics, vol. 48 (1984), no. 2-3, pp. 97108.
[5]Levinski, J.-P., These du Troisieme Cycle, Universite Paris VII, Paris, 1980.
[6]Mitchell, W., in Handbook of Set Theory, to appear.

Related content

Powered by UNSILO

Some pathological examples of precipitous ideals

  • Moti Gitik (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.