Re: Implementable Set Theory and Consistency of ZFC

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

Jesse F. Hughes wrote:

I did not ask about your needs. I asked whether the formula ~Infinity
is also a theorem of (1)-(4), where ~Infinity is the negation of the
axiom of Infinity.

(~Infinity) is _not_ a theorem of (1)-(4), in this article:

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

Why not?

You show that foundation is true in your model. You conclude (1)-(4)
entail foundation.

~Infinity is also true in your model. Why do you not conclude that
(1)-(4) entail ~Infinity?

It is remarkably difficult to get an answer from you sometimes.

Really?

Really.

--
Jesse F. Hughes

"The past two days I haven't had any beer or any wine."
-- Quincy P. Hughes, Age 4 and so damn European
.

Relevant Pages

  • Re: Some basic set theory questions
    ... I disagree with Hughes. ... Axiom of Infinity is required to prove that the empty set ... he'd know that the paper concerns a finitist set theory ... Such a sketch of a single, ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... infinity, where the axiom of infinity is Exe x). ... the negation of the axiom of infinity. ... and Hughes can keep their hands crossed on their stomac and have a flame ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... is also a theorem of -, where ~Infinity is the negation of the ... axiom of Infinity. ... entail foundation. ... Then you cannot prove that adding an axiom to a system of axioms can ...
    (sci.math)
  • Re: abundance of irrationals!)
    ... > Jesse F. Hughes wrote: ... I defined the notation ... > You abused the symbol oo because it is reserved to express infinity. ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... Moeblee and Hughes can keep their hands crossed on their stomac and ... the axiom of Infinity! ... your delusions of grandeur posting on math ...
    (sci.math)