Order Isomorphic

Two totally ordered sets  and  are order isomorphic iff there is a bijection  from  to  such that for all ,

(Ciesielski 1997, p. 38). In other words,  and  are equipollent ("the same size") and there is an order preserving mapping between the two.

Dauben (1990) and Suppes (1972) call this property "similar." The definition works equally well on partially ordered sets.

REFERENCES:

Ciesielski, K. Set Theory for the Working Mathematician. Cambridge, England: Cambridge University Press, 1997.

Dauben, J. W. Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton, NJ: Princeton University Press, 1990.

Mansour, T. "Permutations Avoiding a Pattern from  and at Least Two Patterns from ." 31 Jul 2000. http://arxiv.org/abs/math.CO/0007194.

Suppes, P. Axiomatic Set Theory. New York: Dover, 1972.