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Titlebook: Walks on Ordinals and Their Characteristics; Stevo Todorcevic Book 2007 Birkh?user Basel 2007 Combinatorics.Topology.algebra.coherent mapp

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樓主: Fillmore
51#
發(fā)表于 2025-3-30 10:56:38 | 只看該作者
Stevo TodorcevicOnly full exposition of the method since its invention in the early 1980s.In recent times the method is finding remarkable new appplications.Includes supplementary material:
52#
發(fā)表于 2025-3-30 13:29:22 | 只看該作者
Walks on Countable Ordinals,al essence can be reformulated as problems about ., which is in some sense the smallest uncountable structure. What we mean by ‘structure’ is . together with a system . (. < .) of fundamental sequences, i.e., a system with the following two properties:
53#
發(fā)表于 2025-3-30 17:10:55 | 只看該作者
54#
發(fā)表于 2025-3-30 22:53:48 | 只看該作者
The Square-bracket Operation on Countable Ordinals,(. .) for all . < .. Recall also the notion of the . of the minimal walk, . the finite set of places visited in the minimal walk from . to .. The following simple fact about the upper trace lies at the heart of all known definitions of square-bracket operations, not only on . but also at higher cardinalities.
55#
發(fā)表于 2025-3-31 04:17:43 | 只看該作者
The Square-bracket Operation on Countable Ordinals,(. .) for all . < .. Recall also the notion of the . of the minimal walk, . the finite set of places visited in the minimal walk from . to .. The following simple fact about the upper trace lies at the heart of all known definitions of square-bracket operations, not only on . but also at higher cardinalities.
56#
發(fā)表于 2025-3-31 05:32:59 | 只看該作者
57#
發(fā)表于 2025-3-31 11:37:41 | 只看該作者
Unbounded Functions,essarily coherent, then it is natural to define the corresponding mapping . as follows: . with the boundary value .(.) = 0 for all . < ., a definition that is slightly different from the one given above in (7.3.2) above. Clearly, . and so, using Lemma 6.2.1, we have the following fact.
58#
發(fā)表于 2025-3-31 14:35:25 | 只看該作者
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