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Topic: Order Type
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William Elliot

Posts: 2,360
Registered: 1/8/12
Order Type
Posted: Jun 10, 2014 8:29 AM
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Is this a correct construction of the order type of a well ordered set?

Let S be well ordered, seg_a S = { x in S | a < x }.

Recursively define a function f over S with ordinal values by
f(a) = f(seg_a S) = { f(x) | x < a }.

f is an order isomorphism from S onto the ordianl f(S).

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