
Re: Possible major blunder in Rado's version of Canonical Ramsey Theorem that goes far beyond omitting proof steps
Posted:
Nov 10, 2013 6:02 AM


In message <45d5b7812ea84455b6ffc7ead6d7bd7b@googlegroups.com>, Paul <pepstein5@gmail.com> writes >Agreed that, (when amended using the contributions on this thread), the >newer approach is simpler. But it also proves _far less_. The >original ErdosRado version doesn't assume the axiom of choice >(referred to as "Zermelo's axiom" in that paper). However, the newer >paper does assume the axiom of countable choice by asserting the >existence of B' = {b0, b1...} > >I'm sure that Erdos could have given a particularly simple presentation >if he didn't care about avoiding choice.
I haven't studied the ErdosRado paper in detail, but they state that their proof of the canonical theorem from Ramsey's theorem does not use AC. It is the original proof of Ramsey's theorem which did, but they give a version which avoids it.
Anyway, in the later paper B' is a subset of the natural numbers so no choice axiom is needed to order it.  David Hartley

