Return-Path: Delivery-Date: Received: from ted.cs.uidaho.edu (no rfc931) by swan.cl.cam.ac.uk with SMTP (PP-6.4) outside ac.uk; Wed, 17 Feb 1993 12:00:43 +0000 Received: by ted.cs.uidaho.edu (16.6/1.34) id AA21934; Wed, 17 Feb 93 03:49:40 -0800 Sender: info-hol-request@edu.uidaho.cs.ted Errors-To: info-hol-request@edu.uidaho.cs.ted Precedence: bulk Received: from Maui.CS.UCLA.EDU by ted.cs.uidaho.edu (16.6/1.34) id AA21929; Wed, 17 Feb 93 03:49:35 -0800 Received: from LocalHost.cs.ucla.edu by maui.cs.ucla.edu (Sendmail 5.61d+YP/3.21) id AA21941; Wed, 17 Feb 93 03:49:15 -0800 Message-Id: <9302171149.AA21941@maui.cs.ucla.edu> To: info-hol@edu.uidaho.cs.ted Subject: Re: power of HOL Date: Wed, 17 Feb 93 03:49:14 PST From: chou@edu.ucla.cs Rob Arthan wrote: > Thomas Forster writes: > > Roger has just made the point that HOL is similar in strength to > Zermelo Set Theory. I am pretty sure it is *exactly* equivalent. > At least i cannot see any obvious holes in the obvious proof. > > What is the ``obvious proof''? Indeed, what is the ``obvious proof''? While I can imagine that one can formalize the set-theoretic semantics for HOL given in the Description and construct an interpretation of HOL into ZFC, I can't imagine how the converse can be done. How does one interpret ZFC in HOL? What HOL object would the universe of sets be interpreted into? - Ching Tsun