Re: Implementable Set Theory and Consistency of ZFC

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.

Han de Bruijn

.

Relevant Pages

  • Re: Torkel Franzen on truth
    ... How do you know that ZFC + an axiom of infinity are consistent? ... There are convincing arguments for the ...
    (sci.logic)
  • Re: Orlow cardinality question
    ... >>> I don't simply declare omega to be the smallest infinity. ... In ZFC, it ... You have claimed that ZFC is inconsistant, but so far, ... There are no bigger problems this introduces. ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... ZFC without the axiom of infinity then Choice is _not_ provable ... _is_ provable in ZFC plus the negation of the axiom of infinity. ...
    (sci.math)
  • Re: 1-1/2+1/3-1/4+1/5-1/6+1/7
    ... infinity into one that doesn't. ... I must apologize -- the set theory threads on this ... In the thread titled "Proof that ZFC is inconsistent," ... It's as if F-wit responds ...
    (sci.math)
  • Re: Small set Theory:final version.
    ... Jesse F. Hughes wrote: ... Extensionality: As in ZFC. ... nor it is biconditioned to a predicate in one variable that use x. ...
    (sci.math)