# Journal article

## Structural connections between a forcing class and its modal logic

Abstract:

Every definable forcing class Γ gives rise to a corresponding forcing modality □Γ where □Γφ means that ϕ is true in all Γ extensions, and the valid principles of Γ forcing are the modal assertions that are valid for this forcing interpretation. For example, [10] shows that if ZFC is consistent, then the ZFC-provably valid principles of the class of all forcing are precisely the assertions of the modal theory S4.2. In this article, we prove similarly that the provably valid principles of colla...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
• (Accepted manuscript, pdf, 319.6KB)
Publisher copy:
10.1007/s11856-015-1185-5

### Authors

More by this author
Institution:
University of Oxford
Division:
Humanities Division
Department:
Philosophy
Oxford college:
University College
Role:
Author
Publisher:
Springer Publisher's website
Journal:
Israel Journal of Mathematics Journal website
Volume:
207
Issue:
2
Pages:
617-651
Publication date:
2015-03-28
Acceptance date:
2014-03-20
DOI:
EISSN:
1565-8511
ISSN:
0021-2172
Language:
English
Keywords:
Pubs id:
pubs:916662
UUID:
uuid:0a02eae6-0750-4cc0-9e52-6b0e2dc9ae6e
Local pid:
pubs:916662
Source identifiers:
916662
Deposit date:
2019-12-18

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