Every well-ordered set is uniquely order isomorphic to a unique ordinal number, called the order type of the well-ordered set.
2.
Two partially ordered sets are said to be "'order isomorphic "'when there exists an order isomorphism from one to the other.
3.
One of Baumgartner's results is the consistency of the statement that any two \ aleph _ 1-dense sets of reals are order isomorphic ( a set of reals is \ aleph _ 1-dense if it has exactly \ aleph _ 1 points in every open interval ).
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