| 翻訳と辞書 |
| Morass (set theory) ： ウィキペディア英語版 |
Morass (set theory)
In axiomatic set theory, a mathematical discipline, a morass is an infinite combinatorial structure, used to create "large" structures from a "small" number of "small" approximations. They were invented by Ronald Jensen in his proof that cardinal transfer theorems hold under the axiom of constructibility.
== Overview ==
Whilst it is possible to define so-called gap-''n'' morasses for ''n'' > 1, they are so complex that focus is usually restricted to the gap-1 case, except for specific applications. The "gap" is essentially the cardinal difference between the size of the "small approximations" used and the size of the ultimate structure.
A (gap-1) morass on an uncountable regular cardinal κ consists of a tree of height κ + 1, with the top level having κ+-many nodes. The nodes are taken to be ordinals, and functions π between these ordinals are associated to the edges in the tree order. It is required that the ordinal structure of the top level nodes be "built up" as the direct limit of the ordinals in the branch to that node by the maps π, so the lower level nodes can be thought of as approximations to the (larger) top level node.
A long list of further axioms is imposed to have this happen in a particularly "nice" way.〔K. Devlin. ''Constructibility''. Springer, Berlin, 1984.〕
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
■ウィキペディアで「Morass (set theory)」の詳細全文を読む
スポンサード リンク
| 翻訳と辞書 : 翻訳のためのインターネットリソース |
Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.
|
|