Re: Implementable Set Theory and Consistency of ZFC

On Oct 23, 1:41 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:

Meanwhile, I've _withdrawn_ my claim that ZFC is "inconsistent". Because
that bothers me less than the fact that Infinity is a suspect axiom from
the start. I'm not yet finished with Infinity, though ..

Suppose it is suspect. But you've still not shown how to axiomatize
analysis without it.

a "model" of (ZF-Infinity) is not per se a model of ZFC, which
is the very difference between an "if" and an "iff".

Some models (I have no idea why you put 'model' in scare quotes) of ZF-
I are also models of ZFC and some models of ZF-I are not models of
ZFC. We know the difference between 'if' and 'iff'.

MoeBlee


.

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: Implementable Set Theory and Consistency of ZFC
    ... ZFC without the axiom of infinity then Choice is _not_ provable ... Because (apples without pears) is not the same as (apples without pears ...
    (sci.math)