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Orders of Indescribable Sets
Archive for Mathematical Logic 45 (6):705-714 (2006)
Abstract
We extract some properties of Mahlo’s operation and show that some other very natural operations share these properties. The weakly compact sets form a similar hierarchy as the stationary sets. The height of this hierarchy is a large cardinal property connected to saturation properties of the weakly compact idealOther Versions
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Citations of this work
The weakly compact reflection principle need not imply a high order of weak compactness.Brent Cody & Hiroshi Sakai - 2020 - Archive for Mathematical Logic 59 (1-2):179-196.
Generalisations of stationarity, closed and unboundedness, and of Jensen's □.H. Brickhill & P. D. Welch - 2023 - Annals of Pure and Applied Logic 174 (7):103272.
Adding a Nonreflecting Weakly Compact Set.Brent Cody - 2019 - Notre Dame Journal of Formal Logic 60 (3):503-521.
Forcing a □(κ)-like principle to hold at a weakly compact cardinal.Brent Cody, Victoria Gitman & Chris Lambie-Hanson - 2021 - Annals of Pure and Applied Logic 172 (7):102960.
References found in this work
On splitting stationary subsets of large cardinals.James E. Baumgartner, Alan D. Taylor & Stanley Wagon - 1977 - Journal of Symbolic Logic 42 (2):203-214.
A note on extensions of infinitary logic.Saharon Shelah & Jouko Väänänen - 2005 - Archive for Mathematical Logic 44 (1):63-69.
A Remark on Weakly Compact Cardinals.Tapani Hyttinen - 2002 - Mathematical Logic Quarterly 48 (3):397-402.
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