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Weak commutativity of scattered summation of linear orders. (Russian) Zbl 0441.04003

If \(\alpha\), \(\beta\) are linear order types, then \(\alpha \equiv \beta\) denotes that \(\alpha\) is isomorphically embedded in \(\beta\) and \(\beta\) is isomorphically embedded in \(\alpha\). The following Theorem is proved:
If \(\alpha_i\) \((i\in \beta)\), \(\beta\) a scattered linear order type, then
\[ \Bigl|\bigl\{ j=\sum_{i\in\beta} \alpha_{\pi(i)} \mid \pi \text{ is permutation of } \beta\bigr\}/\equiv\Bigr| \leq |\beta|. \] .
This theorem is a generalization of a theorem of Hickman about ordinals.
Reviewer: A. G. Pinus

MSC:

03E99 Set theory
06A05 Total orders
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