Publikation:

Inner-Model Reflection Principles

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2020

Autor:innen

Caicedo, Andrés Eduardo
Fuchs, Gunter
Hamkins, Joel David
Reitz, Jonas
Schindler, Ralf

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Studia Logica. Springer. 2020, 108(3), pp. 573-595. ISSN 0039-3215. eISSN 1572-8730. Available under: doi: 10.1007/s11225-019-09860-7

Zusammenfassung

We introduce and consider the inner-model reflection principle, which asserts that whenever a statement φ(a) 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 W⊊V. A stronger principle, the ground-model reflection principle, asserts that any such φ(a) 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 Lévy–Montague reflection theorem. They are each equiconsistent with ZFC and indeed Π2-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.

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100 Philosophie

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Inner-model reflection principle, Ground-model reflection principle

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ISO 690BARTON, Neil, Andrés Eduardo CAICEDO, Gunter FUCHS, Joel David HAMKINS, Jonas REITZ, Ralf SCHINDLER, 2020. Inner-Model Reflection Principles. In: Studia Logica. Springer. 2020, 108(3), pp. 573-595. ISSN 0039-3215. eISSN 1572-8730. Available under: doi: 10.1007/s11225-019-09860-7
BibTex
@article{Barton2020-06Inner-52643,
  year={2020},
  doi={10.1007/s11225-019-09860-7},
  title={Inner-Model Reflection Principles},
  number={3},
  volume={108},
  issn={0039-3215},
  journal={Studia Logica},
  pages={573--595},
  author={Barton, Neil and Caicedo, Andrés Eduardo and Fuchs, Gunter and Hamkins, Joel David and Reitz, Jonas and Schindler, Ralf}
}
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