# Sh:383

- Jech, T. J., & Shelah, S. (1993).
*Full reflection of stationary sets at regular cardinals*. Amer. J. Math.,**115**(2), 435–453. arXiv: math/9204218 DOI: 10.2307/2374864 MR: 1216437 -
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. - 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} }