Order isomorphism

between partially ordered sets

A bijection that is also an order-preserving mapping. Order isomorphic sets are said to have the same order type, although this term is often restricted to linearly ordered sets.

Another term is similarity.

References

• Ciesielski, Krzysztof. "Set theory for the working mathematician" London Mathematical Society Student Texts 39 Cambridge University Press (1997) Zbl 0938.03067
• Halmos, Paul R. "Naive Set Theory", Springer (1960, repr. 1974) ISBN 0-387-90092-6 Zbl 0287.04001