Some Pathological Examples of Precipitous Ideals

Journal of Symbolic Logic 73 (2):492 - 511 (2008)
  Copy   BIBTEX

Abstract

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 N₁ • there is no a normal precipitous ideal then there is 0†

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,593

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A model with a precipitous ideal, but no normal precipitous ideal.Moti Gitik - 2013 - Journal of Mathematical Logic 13 (1):1250008.
Precipitous ideals.T. Jech, M. Magidor, W. Mitchell & K. Prikry - 1980 - Journal of Symbolic Logic 45 (1):1-8.
Cardinal preserving ideals.Moti Gitik & Saharon Shelah - 1999 - Journal of Symbolic Logic 64 (4):1527-1551.
The Concept of Ideals in Legal Theory.Sanne Taekema - 2003 - Kluwer Law International.
Economic models of pathological gambling.Don Ross - 2010 - In D. Ross, D. Kincaid, D. Spurrett & P. Collins (eds.), What is Addiction? MIT Press. pp. 131--158.
The entire NS ideal on pγ μ can be precipitous.Noa Goldring - 1997 - Journal of Symbolic Logic 62 (4):1161 - 1172.
On Optimal Development and Becoming an Optimiser.Doret J. Ruyter - 2012 - Journal of Philosophy of Education 46 (1):25-41.
On carcinomas and other pathological entities.Barry Smith, Anand Kumar, Werner Ceusters & Cornelius Rosse - 2005 - Comparative and Functional Genomics 6 (7/8):379–387.
Attractors and pathological aspects in excitable cells.B. Delord - 1999 - Acta Biotheoretica 47 (3-4):239-252.

Analytics

Added to PP
2010-08-24

Downloads
24 (#563,024)

6 months
3 (#445,838)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A model with a precipitous ideal, but no normal precipitous ideal.Moti Gitik - 2013 - Journal of Mathematical Logic 13 (1):1250008.
More on the pressing down game.Jakob Kellner & Saharon Shelah - 2011 - Archive for Mathematical Logic 50 (3-4):477-501.

Add more citations

References found in this work

On generic elementary embeddings.Moti Gitik - 1989 - Journal of Symbolic Logic 54 (3):700-707.

Add more references