# Sh:383

• Jech, T. J., & Shelah, S. (1993). Full reflection of stationary sets at regular cardinals. Amer. J. Math., 115(2), 435–453.
• 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. 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.
• Version 1992-04-01_10 (16p) published version (20p)
Bib entry
@article{Sh:383,
author = {Jech, Thomas J. and Shelah, Saharon},
title = {{Full reflection of stationary sets at regular cardinals}},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {115},
number = {2},
year = {1993},
pages = {435--453},
issn = {0002-9327},
mrnumber = {1216437},
mrclass = {03E35 (03E05 03E55)},
doi = {10.2307/2374864},
note = {\href{https://arxiv.org/abs/math/9204218}{arXiv: math/9204218}},
arxiv_number = {math/9204218}
}