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On a relation between $\lambda$-full well-ordered sets and weakly compact cardinals
- Publication Year :
- 2024
-
Abstract
- We prove, via transfinite recursion, the existence, inside any linearly ordered set of appropriate regular cardinality $\lambda$, of a particular kind of well-ordered subsets characterized by the property of $\lambda$-fullness. Let $H$ be a set of regular cardinals: by using our results about well-ordered $\lambda$-full sets we show that if $\inf H$ is a weakly compact cardinal, then, for every LOTS $X$, $H$-compactness is equivalent to the nonexistence of gaps of types in $H$.
- Subjects :
- Mathematics - Logic
Mathematics - General Topology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2403.15904
- Document Type :
- Working Paper