Meaning of order type | Babel Free

Definitions

In the context of sets equipped with an order (especially, the context of totally ordered sets), the characteristic of being a member of some equivalence class of such sets under the equivalence relation "existence of an order-preserving bijection".

Examples

“1965 [John Wiley], Raymond L. Wilder, Introduction to the Foundations of Mathematics: 2nd Edition, 2012, Dover, page 116, Another way of putting this is to state that the order⟳ type⟳ is that aspect of the arrangement of the elements of a simply ordered set⟳, which remains unchanged when any two elements are exchanged. […] As in the case of cardinal numbers, order⟳ types may be denoted by suitable symbols called ordinal numerals.”

“In [13] Chajoth studied how the order⟳ type⟳ of a chain can alter if we change⟳ the position of elements in a linearly ordered set⟳, resp. if we introduce⟳ a new element in a linearly ordered set⟳.”

“2011, Douglas Cenzer, Valentina Harizanov, Jeffrey B. Remmel, Effective Categoricity of Injection Structures, Benedikt Löwe, Dag Normann, Ivan Soskov, Alexandra Soskova (editors, Models of Computation in Context: 7th Conference on Computability in Europe, CiE 2011, Proceedings, Springer, LNCS 6735, page 51, We let⟳ ω denote the order⟳ type⟳ of N under the usual ordering and Z denote the order⟳ type⟳ of Z under the usual ordering.”

CEFR level