| 词条 | Ulam matrix |
| 释义 |
In mathematical set theory, an Ulam matrix is an array of subsets of a cardinal number with certain properties. Ulam matrices were introduced by {{harvs|txt|last=Ulam|authorlink=S. Ulam|year=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] DefinitionSuppose 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
References1. ^{{citation | last1=Jech | first1=Thomas | author1-link=Thomas Jech | title=Set Theory | edition=Third Millennium | publisher=Springer-Verlag | location=Berlin, New York | series=Springer Monographs in Mathematics | isbn=978-3-540-44085-7 | year=2003 | zbl=1007.03002 | page=131 }}
|year=1930 |volume= 16 |issue=1 |pages= 140–150 |title=Zur Masstheorie in der allgemeinen Mengenlehre |first=Stanisław |last=Ulam|url=http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-fmv16i1p14bwm?q=2c1badc7-22c8-4f89-a9de-dee5818f5258$8&qt=IN_PAGE }}{{settheory-stub}} 1 : Set theory |
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