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THE DIAGONAL STRONG REFLECTION PRINCIPLE AND ITS FRAGMENTS

Part of: Set theory

Published online by Cambridge University Press:  10 January 2023

SEAN D. COX Open the ORCID record for SEAN D. COX [Opens in a new window]  and
GUNTER FUCHS Open the ORCID record for GUNTER FUCHS [Opens in a new window]
SEAN D. COX
Affiliation:
DEPARTMENT OF MATHEMATICS AND APPLIED MATHEMATICS VIRGINIA COMMONWEALTH UNIVERSITY 1015 FLOYD AVENUE RICHMOND, VA 23284, USA E-mail: scox9@vcu.edu
GUNTER FUCHS*
Affiliation:
THE COLLEGE OF STATEN ISLAND THE CITY UNIVERSITY OF NEW YORK 2800 VICTORY BOULEVARD STATEN ISLAND, NY 10314, USA and THE GRADUATE CENTER THE CITY UNIVERSITY OF NEW YORK 365 FIFTH AVENUE NEW YORK, NY 10016, USA URL: www.math.csi.cuny.edu/~fuchs
*
E-mail: gunter.fuchs@csi.cuny.edu
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Abstract

A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated with arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the corresponding forcing axioms and the corresponding fragments of the strong reflection principle, are analyzed, and consequences are presented. Some of these consequences are “exact” versions of diagonal stationary reflection principles of sets of ordinals. We also separate some of these diagonal strong reflection principles from related axioms.

Keywords

forcing axiomsreflection principlesstrong reflection principlediagonal reflection

MSC classification

Primary: 03E57: Generic absoluteness and forcing axioms 03E50: Continuum hypothesis and Martin's axiom 03E35: Consistency and independence results 03E75: Applications of set theory

Information

Type
Article
Information
The Journal of Symbolic Logic , Volume 88 , Issue 3 , September 2023 , pp. 1281 - 1309
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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