From: Thomas Streicher <streicher@mathematik.tu-darmstadt.de>
To: categories@mta.ca
Subject: when are Lindenbaum-Tarski algebras complete?
Date: Wed, 21 Nov 2007 15:33:32 +0100 (CET) [thread overview]
Message-ID: <E1IuwBs-0006mx-Kw@mailserv.mta.ca> (raw)
I also suspect that Sub(1) of the free topos with nno is not complete.
But countability does not suffice for refuting completeness (the ordinal
\omega + 1 is an infinite countable cHa which nevertheless is complete).
>From Goedel's Theorem for HAH (higher order intuit. arithmetic) it follows
that Sub(1) of the free topos with nno is not atomic. But that also doesn't
suffice for refuting completeness.
On p.169 of Freyd, Friedman and Scedrov's paper
"Lindenbaum algebras of intuitionistic theories and free categories" (APAL 35)
they claim "Lindenbaum algebras are almost never complete" but don't give
a proof.
Thomas Streicher
next reply other threads:[~2007-11-21 14:33 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2007-11-21 14:33 Thomas Streicher [this message]
2007-11-21 21:30 Dana Scott
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