Re: How many different unit fractions are lessorequal than all unit fractions?

On 9/22/2024 9:22 AM, WM wrote:

On 22.09.2024 00:32, Jim Burns wrote:

On 9/21/2024 4:11 PM, WM wrote:

On 21.09.2024 19:26, Jim Burns wrote:

There is no transfinite WWMB ordinal ξ before
the first transfinite ordinal, WWMB ω

>
That may be. But then
there is no complete set of natural numbers
and no ω.

>
WWMB ω is the first transfinite ordinal.
Existing or not.existing, WWMB ω isn't
anything other than the first transfinite ordinal.
>
As long as it's WWMB ω which you discuss,
WWMB ω-1 doesn't exist.

>
Then ω does not exist.

If
we are discussing
Boolos's ST with plural quantification,
⎛ ∃{}
⎜ ∃z=x∪{y}
⎝ ∀.extensionality
⎛ ∃∃⦃y:P(y)⦄
⎜ ∀x:  x ∈ ⦃y:P(y)⦄  ⇔  P(x)
⎝ ∀∀.extensionality
then
there is WWMB ω = ⦃y:ℕ(y)⦄ and
there isn't WWMB ω-1 such that (ω-1)+1 = ω
Which of  {}  x∪{y}  ⦃y:P(y)⦄
do you deny exists?