Journal article
Inter-model reflection principles
- Abstract:
- We introduce and consider the inner-model reflection principle, which asserts that whenever a statement ๐(๐) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model ๐โ๐. A stronger principle, the ground-model reflection principle, asserts that any such ๐(๐) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width reflection in contrast to the usual height reflection of the LรฉvyโMontague reflection theorem. They are each equiconsistent with ZFC and indeed ฮ 2-conservative over ZFC, being forceable by class forcing while preserving any desired rank-initial segment of the universe. Furthermore, the inner-model reflection principle is a consequence of the existence of sufficient large cardinals, and lightface formulations of the reflection principles follow from the maximality principle MP and from the inner-model hypothesis IMH. We also consider some questions concerning the expressibility of the principles.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 367.5KB, Terms of use)
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- Publisher copy:
- 10.1007/s11225-019-09860-7
Authors
- Publisher:
- Springer
- Journal:
- Studia Logica More from this journal
- Volume:
- 108
- Issue:
- 3
- Pages:
- 573-595
- Publication date:
- 2019-04-20
- Acceptance date:
- 2018-09-06
- DOI:
- EISSN:
-
1572-8730
- ISSN:
-
0039-3215
- Language:
-
English
- Keywords:
- Pubs id:
-
997903
- Local pid:
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pubs:997903
- Deposit date:
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2020-11-30
- ARK identifier:
Terms of use
- Copyright holder:
- Barton et al.
- Copyright date:
- 2020
- Rights statement:
- ยฉ The Author(s) 2019. Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the articleโs Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the articleโs Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
- Licence:
- CC Attribution (CC BY)
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