Ulam matrix
From Infogalactic: the planetary knowledge core
In mathematical set theory, an Ulam matrix is an array of subsets of a cardinal number with certain properties. Ulam matrices were introduced by Ulam (1930) in his work on measurable cardinals: they may be used, for example, to show that a real-valued measurable cardinal is weakly inaccessible.[1]
Definition
Suppose that κ and λ are cardinal numbers, and let F be a λ-complete filter on λ. An Ulam matrix is a collection of subsets Aαβ of λ indexed by α in κ, β in λ such that
- If β is not γ then Aαβ and Aαγ are disjoint.
- For each β the union of the sets Aαβ is in the filter F.
References
- ↑ Lua error in package.lua at line 80: module 'strict' not found.
- Lua error in package.lua at line 80: module 'strict' not found.
<templatestyles src="Asbox/styles.css"></templatestyles>
 |
This set theory-related article is a stub. You can help Wikipedia by expanding it. |
