Re: Implementable Set Theory and Consistency of ZFC

Jesse F. Hughes wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Jesse F. Hughes wrote:

Han.deBruijn@xxxxxxxxxxxxxx writes:

On 18 okt, 19:52, "Jesse F. Hughes" <je...@xxxxxxxxxxxxx> wrote:

It's not clear to me what the last claim means, but regardless, it
must mean something about "all sets" in this particular model of
ZFC - Infinity and not all sets of ZFC.

No. It's about all sets in (ZFC - Infinity). And the "particular
model" is any implementation, is anything applicable.

I guess you mean ZFC - Infinity + ~Infinity, since there are models
of
ZFC - Infinity that have infinite sets.

It's impossible to have infinity without Infinity. If not, show us such
a model, please.

Any model for ZFC is a model for ZFC - Infinity. Why? Because it
satisfies every axiom for ZFC - Infinity.

As I said, what you must mean is ZFC - Infinity + ~Infinity. That is,
take ZFC, remove the axiom of infinity and add the negation of the
axiom of infinity.

Not in my article:

http://hdebruijn.soo.dto.tudelft.nl/jaar2007/set_theory.pdf

Han de Bruijn

.

Relevant Pages