Definition:Order Property
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Definition
An order property is a property of an ordered sets which is invariant under order isomorphism.
That is, if $\struct {S_1, \preceq_1}$ and $\struct {S_2, \preceq_2}$ are isomorphic ordered sets, and $P$ is a property, then:
- $\map P {S_1, \preceq_1} \iff \map P {S_2, \preceq_2}$
Also see
- Results about order properties can be found here.
Sources
- 1996: Winfried Just and Martin Weese: Discovering Modern Set Theory. I: The Basics ... (previous) ... (next): Part $1$: Not Entirely Naive Set Theory: Chapter $2$: Partial Order Relations