0

Sometimes it's better to see once than to say a thousand words.
Following link shows what ordinals really looks like :

Ordinal tetration: The issue of ${}^{\epsilon_0}\omega$

And following is a screenshot of above link.

enter image description here

So the answerer couldn't(or didn't) show small veblen or large veblen ordinal in similar form.

Q1) Can you express small or large veblen ordinal in this form ?

Q2) Is it possible to define mathematically rigorously following statement? Then how far can we express in such form ?

+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
An ordianl O can be expressed using

integers $\omega$
...... (the repeating symbol)
addition
multiplication
exponentiation
up-arrow symbol
other symbols?(maybe some steps further than up-arrow symbol?)
+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

Q3) Can you express bachmann-howard ordinal in this form, not using any big (bigger than $\omega$) ordinals ?

imida k
  • 295
  • upvoted this one – mick Nov 22 '23 at 12:11
  • Patterns can be extended in more than one way, so what would be the meaning of some expression such as "$\omega\uparrow^2(\omega\uparrow^1\uparrow(\omega\uparrow^{17}\ldots))$"? – C7X Feb 10 '24 at 01:32

0 Answers0