We investigate the properties of ideals such that their corresponding partial orders preserve stationarity. We show that these ideals exhibit many large cardinal-like consequences. We also prove the existence of a certain non-reflecting stationary subset of under some hypotheses.
Yo MATSUBARA. "Stationary preserving ideals over ." J. Math. Soc. Japan 55 (3) 827 - 835, July, 2003. https://doi.org/10.2969/jmsj/1191419004