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Re: [Coq-Club] Axiom of choice

From: Andrej Bauer <Andrej.Bauer AT andrej.com>
Cc: coq-club AT pauillac.inria.fr, Adam Chlipala <adamc AT hcoop.net>, Elnatan Reisner <elnatan AT cs.umd.edu>
Subject: Re: [Coq-Club] Axiom of choice
Date: Thu, 28 Aug 2008 10:39:42 +0200
List-archive: <http://pauillac.inria.fr/pipermail/coq-club/>

Andrej Bauer wrote:
> In general, a setting which separates logic and type theory will fail to
> prove axiom of choice. This is visible in Coq which distinguishes
> between Set and Prop.

I forgot to point out what the difference between Set and Prop is: the
latter has proof irrelevance. Coq achieves proof irrelevance by imposing
restrictions on maps from Prop to Set.

Andrej

[Coq-Club] Axiom of choice, Elnatan Reisner
- Re: [Coq-Club] Axiom of choice, Adam Chlipala
  - Re: [Coq-Club] Axiom of choice, Andrej Bauer
    - Re: [Coq-Club] Axiom of choice, Andrej Bauer
    - Re: [Coq-Club] Axiom of choice, Thorsten Altenkirch