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To: info-hol%clover.ucdavis.edu@NSFnet-Relay.AC.UK
Cc: ap%computer-lab.cambridge.ac.uk@NSFnet-Relay.AC.UK
Subject: Re: Semantics of HOL
Date: Mon, 09 Apr 90 10:20:40 +0100
From: ap%computer-lab.cambridge.ac.uk@NSFnet-Relay.AC.UK
Message-Id:  <9004091020.aa02448@gnnt.Cl.Cam.AC.UK>

> In response to Josh Guttman's question: ...
> ..., I would think.
> Andrew Pitts has a paper on the semantics of HOL.
>
> Francisco

The paper referred to is in fact Chapter 10 in Volume 2 (Description)
of the current HOL documentation. I should warn anyone turning to it in
response to Josh Guttman's question, that the chapter's only aim is to
describe a standard (intended) set-theoretic model of HOL, which
certainly is "full" in the sense of Josh's message.  The chapter does
not address what constitutes a model in general, be it Henkin-style or
something more general still, eg category-theoretic. With regard to the
latter, let me put in a plug for a nice book

JL Bell, Toposes and local Set Theories, An Introduction. Oxford Logic
Guides 14 (OUP, 1988)

The "local set theory" referred to in the title  is a form of
constructive, rather than classical, higher-order logic, but
semantically-oriented HOLers may find it interesting.

Andy Pitts

