Can a large cardinal be forced from a condition implying its negation?

Arthur W. Apter; Grigor Sargsyan

doi:10.1090/S0002-9939-05-07840-8

Can a large cardinal be forced from a condition implying its negation?

Arthur W. Apter, Grigor Sargsyan

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this note, we provide an affirmative answer to the title question by giving two examples of cardinals satisfying conditions implying they are non-Rowbottom which can be turned into Rowbottom cardinals via forcing. In our second example, our cardinal is also non-Jonsson.

Original language	English (US)
Pages (from-to)	3103-3108
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	133
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-05-07840-8
State	Published - Oct 2005
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Keywords

Jonsson cardinal
Rowbottora cardinal
Strongly compact cardinal

Access to Document

10.1090/S0002-9939-05-07840-8

Cite this

@article{17bcf02b28b34936ae9ed5826cff08c2,

title = "Can a large cardinal be forced from a condition implying its negation?",

abstract = "In this note, we provide an affirmative answer to the title question by giving two examples of cardinals satisfying conditions implying they are non-Rowbottom which can be turned into Rowbottom cardinals via forcing. In our second example, our cardinal is also non-Jonsson.",

keywords = "Jonsson cardinal, Rowbottora cardinal, Strongly compact cardinal",

author = "Apter, {Arthur W.} and Grigor Sargsyan",

year = "2005",

month = oct,

doi = "10.1090/S0002-9939-05-07840-8",

language = "English (US)",

volume = "133",

pages = "3103--3108",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",