I always thought all platonic realms are flooded with light!
Now something from the formalists that want to
to capture the light. It seems to me ordinals
are a forgotten treasure. Nice papers here:
W. A. Howard: Assignment of ordinals to terms for
primitive recursive functionals of finite type.
Howard, William A. (September 1970)
https://www.sciencedirect.com/science/article/abs/pii/S0049237X08707705
Systems of logic based on ordinals
Alan Touring - 1938 (sic!)
https://people.math.ethz.ch/~halorenz/4students/Literatur/TuringOrdinalLogic.pdf
Homework for Dan Christensen:
- Show PA consistent (in ZFC).
WM schrieb:
Le 22/02/2024 à 17:13, Jim Burns a écrit :
On 2/22/2024 8:00 AM, WM wrote:
Le 21/02/2024 à 18:59, Jim Burns a écrit :
On 2/21/2024 3:33 AM, WM wrote:
Le 20/02/2024 à 23:02, Jim Burns a écrit :
Ordinals are well.ordered.
Only those which can be specified.
No.
All of them are well.ordered.
How do you know?
In the same way that I know
that right.triangles have three corners.
Yes, you are right. I exaggerated. Having three corners is essential
for triangles. Being well-ordered is essential for ordinals. What I
meant is that we cannot follow the well-order into the dark realm. In particular Peano ceases.
Regards, WM
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