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

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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DOI 10.1007/BF01270466
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References found in this work BETA

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.
The Fine Structure of the Constructible Hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.
A New Class of Order Types.James E. Baumgartner - 1976 - Annals of Mathematical Logic 9 (3):187-222.

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Citations of this work BETA

Adding a Nonreflecting Weakly Compact Set.Brent Cody - 2019 - Notre Dame Journal of Formal Logic 60 (3):503-521.
Orders of Indescribable Sets.Alex Hellsten - 2006 - Archive for Mathematical Logic 45 (6):705-714.
Characterizations of the Weakly Compact Ideal on Pλ.Brent Cody - 2020 - Annals of Pure and Applied Logic 171 (6):102791.

View all 7 citations / Add more citations

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