𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Remark on Weakly Compact Cardinals

✍ Scribed by Tapani Hyttinen

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
134 KB
Volume
48
Category
Article
ISSN
0044-3050

No coin nor oath required. For personal study only.

✦ Synopsis

We show that if ΞΊ is weakly compact, then ΞΊ β†’ (stationary, ΞΊ) 3 holds for treelike partitions. As an application we study model constructions.

πŸ“œ SIMILAR VOLUMES

On Compact Cardinals
On Compact Cardinals
✍ J. L. Bell πŸ“‚ Article πŸ“… 1974 πŸ› John Wiley and Sons 🌐 English βš– 332 KB

ON COMPACT CARDINALS by J. L. BELL in London (Great Britain) Let x be a cardinal and L a language. x is said to be L-compact if whenever ,Z is a set of sentences of L such that any subset of L' of power < x has a model, so does Z. If 9 is a class of languages, we say that x is 9-compact if x is L-co

Weakly measurable cardinals
Weakly measurable cardinals
✍ Jason A. Schanker πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 194 KB

In this article, we introduce the notion of weakly measurable cardinal, a new large cardinal concept obtained by weakening the familiar concept of a measurable cardinal. Specifically, a cardinal ΞΊ is weakly measurable if for any collection A containing at most ΞΊ + many subsets of ΞΊ, there exists a n

More on the Least Strongly Compact Cardi
More on the Least Strongly Compact Cardinal
✍ Arthur W. Apter πŸ“‚ Article πŸ“… 1997 πŸ› John Wiley and Sons 🌐 English βš– 229 KB

## Abstract We show that it is consistent, relative to a supercompact limit of supercompact cardinals, for the least strongly compact cardinal k to be both the least measurable cardinal and to be > 2^k^ supercompact.