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From: play@mcvax.UUCP (Andries Brouwer)
Newsgroups: net.math
Subject: Re: Re: truth of CH
Message-ID: <538@mcvax.UUCP>
Date: Sun, 17-Mar-85 21:08:51 EST
Article-I.D.: mcvax.538
Posted: Sun Mar 17 21:08:51 1985
Date-Received: Tue, 19-Mar-85 08:14:06 EST
References: <143@ihlpa.UUCP> <460@petsd.UUCP> <6353@boring.UUCP> <350@talcott.UUCP> <529@mcvax.UUCP> <359@talcott.UUCP>
Reply-To: play@mcvax.UUCP (Andries Brouwer)
Organization: CWI, Amsterdam
Lines: 15

In article <359@talcott.UUCP> gjk@talcott.UUCP (Greg Kuperberg) writes:
>> ... the current inference rules already allow you to
>> construct models in which CH holds and models in which it doesnt hold.
>> Stronger inference rules deciding CH would thus lead to a contradiction.
>
>I don't see the contradication.  With the old inference rules, both models
>are valid, while with the new inference rules, only one of them is.  What
>is wrong with that?
>
What is a valid model? It is one satisfying the imposed axioms.
Inference rules tell you how to get valid statements from other valid
statements, but have no direct bearing on models, except in that one
never could accept a rule of inference when there exist models satisfying
the input formulas but not the output formulas of the rule.
That is why CH cannot be decided by stronger inference rules.