Exactly controlling the non-supercompact strongly compact cardinals

Apter, Arthur W.; Hamkinks, Joel David

J. Symbolic Logic, Tome 68 (2003) no. 1, p. 669- 688 / Harvested from Project Euclid

Résumé

We summarize the known methods of producing a non-supercompact strongly compact cardinal and describe some new variants. Our Main Theorem shows how to apply these methods to many cardinals simultaneously and exactly control which cardinals are supercompact and which are only strongly compact in a forcing extension. Depending upon the method, the surviving non-supercompact strongly compact cardinals can be strong cardinals, have trivial Mitchell rank or even contain a club disjoint from the set of measurable cardinals. These results improve and unify Theorems 1 and 2 of [A97], due to the first author.

Publié le : 2003-06-14
Classification:

@article{1052669070,
     author = {Apter, Arthur W. and Hamkinks, Joel David},
     title = {Exactly controlling the non-supercompact strongly compact cardinals},
     journal = {J. Symbolic Logic},
     volume = {68},
     number = {1},
     year = {2003},
     pages = { 669- 688},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1052669070}
}

Apter, Arthur W.; Hamkinks, Joel David. Exactly controlling the non-supercompact strongly compact cardinals. J. Symbolic Logic, Tome 68 (2003) no. 1, pp.  669- 688. http://gdmltest.u-ga.fr/item/1052669070/