[FOM] First, second order theories, second order characterizations

Alasdair Urquhart urquhart at cs.toronto.edu
Sun Sep 8 12:15:01 EDT 2013

Georg Kreisel in "Informal Rigour and Completeness Proofs" argues that
CH is decided by second order ZFC (not that it is an axiom of this
system), and hence that it has a truth-value in some
absolute sense.

There is a critical article on Kreisel's argument by
Thomas Weston:

 	"Kreisel, the continuum hypothesis and second order set theory"
 	Journal of Philosophical Logic, Volume 5, pp. 281-298.

Weston's criticisms seem on the mark to me.

On Sat, 7 Sep 2013, Harvey Friedman wrote:

> In http://www.cs.nyu.edu/pipermail/fom/2013-August/017552.html
> I asked
> 1. Is CH an axiom of ZFC?
> 2. Is CH an "axiom" of second order ZFC"?
> 3. Is CH a theorem of ZFC?
> 4. Is CH an "axiom of second order ZFC"?
> The main point of these questions is to flesh out apparent confusions I am seeing on the FOM concerning so called  "second order systems". 

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