Abstract
We introduce a natural two-cardinal version of Bagaria’s sequence of derived topologies on ordinals. We prove that for our sequence of two-cardinal derived topologies, limit points of sets can be characterized in terms of a new iterated form of pairwise simultaneous reflection of certain kinds of stationary sets, the first few instances of which are often equivalent to notions related to strong stationarity, which has been studied previously in the context of strongly normal ideals. The non-discreteness of these two-cardinal derived topologies can be obtained from certain two-cardinal indescribability hypotheses, which follow from local instances of supercompactness. Additionally, we answer several questions posed by the first author, Holy and White on the relationship between Ramseyness and indescribability in both the cardinal context and in the two-cardinal context.
Original language | English |
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Journal | Journal of Symbolic Logic |
DOIs | |
State | Accepted/In press - 2024 |
Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2024 Cambridge University Press. All rights reserved.
Keywords
- Ramsey cardinals
- Ramsey hierarchy
- derived topology
- indescribable cardinals
- stationary reflection