Full Reflection at a Measurable Cardinal

Details Full Reflection at a Measurable Cardinal Full Reflection at a Measurable Cardinal

1993-02-25

arxiv.org/abs/math/9302202v1

Mathematics

Logic

Scientific paper

A stationary subset $S$ of a regular uncountable cardinal $\kappa$ {\it 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 $\alpha$. {\it Full Reflection} states that every stationary set reflects fully at regular cardinals. We will prove that under a slightly weaker assumption than $\kappa$ having Mitchell order $\kappa^{++}$ it is consistent that Full Reflection holds at every $\lambda \leq \kappa$ and $\kappa$ is measurable.

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