# Re: Cardinality vs Subsets

*From*: FredJeffries <fredjeffries@xxxxxxxxx>*Date*: Thu, 24 Feb 2011 05:43:28 -0800 (PST)

On Feb 22, 1:45 pm, Transfer Principle <lwal...@xxxxxxxxx> wrote:

On Feb 22, 4:05 am, Math1723 <anonym1...@xxxxxxx> wrote:

On Feb 22, 1:52 am, Transfer Principle <lwal...@xxxxxxxxx> wrote:

I fully accept that Cantor's theorem is a theorem of ZFC. But notSpeaking of which, have you determined which of the nine specific ZFC

everyone wants to be, or should be, bound by what ZFC proves. So

those who don't can choose a set theory, such as NFU, in which

Cantor isn't a theorem (assuming consistency), or search for a

new theory in which the negation of Cantor is provable.

axioms [snip link] that you have a problem with?

For the vast majority of posters who criticize ZFC, the axiom

that they have a problem with is the Axiom of Infinity. It's

Infinity that leads directly to the results that such posters

are trying to avoid.

(Perhaps occasionally, a poster who accepts infinite sets but

not uncountable sets might be satisfied by dropping Powerset

rather than Infinity, but this is rare.)

Edward Belaga would allow countable, but not uncountable, ordinals:

http://www-irma.u-strasbg.fr/~belaga/

http://www-irma.u-strasbg.fr/~belaga/4*MathInfinity.pdf

http://arxiv.org/PS_cache/arxiv/pdf/0812/0812.3207v3.pdf

http://www-irma.u-strasbg.fr/~belaga/HalfwayUpToTheMathematicalInfinityIII_SPUC09slides090324.pptx

"Are we really living in the world where the Power-Set Axiom is a

universal mathematical truth?" II. Proc. of the 17th Congress of the

Canadian Society of History and Philosophy of Mathematics, eds. H.

Grant et al., Kingston, May (1991)

.

**References**:**Cardinality vs Subsets***From:*Math1723

**Re: Cardinality vs Subsets***From:*Daryl McCullough

**Re: Cardinality vs Subsets***From:*Dick

**Re: Cardinality vs Subsets***From:*Jesse F. Hughes

**Re: Cardinality vs Subsets***From:*Transfer Principle

**Re: Cardinality vs Subsets***From:*Math1723

**Re: Cardinality vs Subsets***From:*Transfer Principle

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