Pinus, A. G. Weak commutativity of scattered summation of linear orders. (Russian) Zbl 0441.04003 Sib. Mat. Zh. 21, No. 2, 155-159 (1980). 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 Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 Review MSC: 03E99 Set theory 06A05 Total orders Keywords:linear order types; ordinals PDFBibTeX XMLCite \textit{A. G. Pinus}, Sib. Mat. Zh. 21, No. 2, 155--159 (1980; Zbl 0441.04003) Full Text: EuDML