### Full reflection of stationary sets at regular cardinals

by Jech and Shelah. [JeSh:383]

American J Math, 1993

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 . We prove that the Axiom of Full
Reflection which states that every stationary set reflects fully at
regular cardinals, together with the existence of n-Mahlo
cardinals is equiconsistent with the existence of
Pi^1_n-indescribable cardinals. We also state the appropriate
generalization for greatly Mahlo cardinals.

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