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Rigidity in order-types
Published online by Cambridge University Press: 09 April 2009
Abstract
A totally ordered set (and corresponding order-type) is said to be rigid if it is not similar to any proper initial segment of itself. The class of rigid ordertypes is closed under addition and multiplication, satisfies both cancellation laws from the left, and admits a partial ordering that is an extension of the ordering of the ordinals. Under this ordering, limits of increasing sequences of rigid order-types are well defined, rigid and satisfy the usual limit laws concerning addition and multiplication. A decomposition theorem is obtained, and is used to prove a characterization theorem on rigid order-types that are additively prime. Wherever possible, use of the Axiom of Choice is eschewed, and theorems whose proofs depend upon Choice are marked.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 24 , Issue 2 , September 1977 , pp. 203 - 215
- Copyright
- Copyright © Australian Mathematical Society 1977
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