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- Newsgroups: sci.math
- Path: sparky!uunet!decwrl!world!rjk
- From: rjk@world.std.com (robert j kolker)
- Subject: Order -> Algebraic Structure
- Message-ID: <BvvuD8.I26@world.std.com>
- Summary: Is there a way to get from order to algebraic structure?
- Keywords: Rationals,Dense Ordering,Algebraic Structure
- Organization: The World Public Access UNIX, Brookline, MA
- Date: Sat, 10 Oct 1992 01:48:43 GMT
- Lines: 18
-
- Let H be a denumerable completely ordered set, where the ordering is
- dense, and there are no maximum or minumum elements. It is well known that
- any two sets having these properties are order isomorphic.
-
- The set of rationals Q is a fortiori this set (up to an isomorphism).
- Clearly the seemingly innocent densely ordered set inherits its algebraic
- properties via this isomorphism or does it?
-
- Is there someway of showing independent of this coincidental isomorphism ,
- that denumerable,densely ordered -> the algebraic structure of Q, i.e. Q
- is a denumerable field or characteristic 0.
-
- Your input would be appreciated.
-
- Conan the Libertarian rjk@world.std.com
- "If you can't love the Constitution, at least hate the Government"
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