Journal of Symbolic Logic

Full Reflection at a Measurable Cardinal

Thomas Jech and Jiri Witzany

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Abstract

A stationary subset $S$ of a regular uncountable cardinal $\kappa$ reflects fully at regular cardinals if for every stationary set $T \subseteq \kappa$ of higher order consisting of regular cardinals there exists an $\alpha \in T$ such that $S \cap \alpha$ is a stationary subset of $\alpha$. Full Reflection states that every stationary set reflects fully at regular cardinals. We will prove that under a slightly weaker assumption than $\kappa$ having the Mitchell order $\kappa^{++}$ it is consistent that Full Reflection holds at every $\lambda \leq \kappa$ and $\kappa$ is measurable.

Article information

Source
J. Symbolic Logic, Volume 59, Issue 2 (1994), 615-630.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183744503

Mathematical Reviews number (MathSciNet)
MR1276638

Zentralblatt MATH identifier
0799.03060

JSTOR
links.jstor.org

Subjects
Primary: 03E35: Consistency and independence results
Secondary: 03E55: Large cardinals

Keywords
Stationary sets full reflection measurable cardinals repeat points

Citation

Jech, Thomas; Witzany, Jiri. Full Reflection at a Measurable Cardinal. J. Symbolic Logic 59 (1994), no. 2, 615--630. https://projecteuclid.org/euclid.jsl/1183744503


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