From: Brandsma <brandsma@twi.tudelft.nl>
Subject: Re: fan theorem
Date: Fri, 16 Jul 1999 09:13:52 +0200
Newsgroups: sci.math
Keywords: graphs with bounded length

Mark wrote:

> Hello everybody !
> Recently I read about the fan theorem. Can anyone give me hints for
> literature ? (please NO raph theory) especiallly : Is there a hole thory
> on fans available yet ?
> Thanky in advance,
>
> Markus

There is a theorem, equivalent to Ko"nig's theorem on graphs, that is called
the fan theorem. A fan is a finitely branching tree, so every node has
finitely many successors. The theorem then says: if all branches of a fan
are finite, then there lenghts must be bounded. (Ko"nig's theorem says that
an infinite fan has an infinite path). I know this terminology from some of
my books on logic, e.g. van Dalen "logic and structure". (he claims the fan
theorem is older than Ko"nig's, and proves the result by compactness of
first order logic.

Henno Brandsma