Stationary Cardinals

Archive for Mathematical Logic 32 (6):429-442 (1993)
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Abstract

This paper will define a new cardinal called aStationary Cardinal. We will show that every weakly∏ 1 1 -indescribable cardinal is a stationary cardinal, every stationary cardinal is a greatly Mahlo cardinal and every stationary set of a stationary cardinal reflects. On the other hand, the existence of such a cardinal is independent of that of a∏ 1 1 -indescribable cardinal and the existence of a cardinal such that every stationary set reflects is also independent of that of a stationary cardinal. As applications, we will show thatV=L implies ◊ κ 1 holds if κ is∏ 1 1 -indescribable and so forth

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Citations of this work

Characterizations of the weakly compact ideal on Pλ.Brent Cody - 2020 - Annals of Pure and Applied Logic 171 (6):102791.
Higher indescribability and derived topologies.Brent Cody - 2023 - Journal of Mathematical Logic 24 (1).
Small models, large cardinals, and induced ideals.Peter Holy & Philipp Lücke - 2021 - Annals of Pure and Applied Logic 172 (2):102889.

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References found in this work

Some exact equiconsistency results in set theory.Leo Harrington & Saharon Shelah - 1985 - Notre Dame Journal of Formal Logic 26 (2):178-188.
Reflecting stationary sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
A new class of order types.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (3):187-222.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
Multiple Forcing.T. Jech - 1989 - Journal of Symbolic Logic 54 (3):1112-1113.

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