Fast growing hierarchies, ordinal collapsing and Pi^1_1-CA_0
Andreas Weiermann
Andreas.Weiermann at UGent.be
Mon Oct 18 16:48:44 EDT 2021
Dear FOM'ers,
maybe the following seminar is of interest for some of you:
On Wednesday 20 October 2021 09:00-10:00 UTC Fedor Pakhomov will speak about
"Fast growing hierarchies, ordinal collapsing and Pi^1_1-CA_0"
The abstract is:
Weakly finite dilators are functions F from naturals to naturals for
which we have a fixed extension to a dilator F:On->On. We show that for
a large class of natural ordinal notation systems α the fast growing
function F_α naturally could be treated as a weakly finite dilator. More
precisely our construction works when α=D(ω), for a weakly finite
dilator D. Thus we have an operator that maps a weakly finite dilator D
to the weakly finite dilator F_{D(ω)}. We show that F_{D(ω)} could be
naturally identified with the ordinal denotation system based on a
variant of collapsing function ψ, collapsing D(Ω). We show that the fact
that this operator maps weakly finite dilators to weakly finite dilators
is equivalent to Π¹₁-CA₀.
(This is joint work with Juan Pablo Aguilera and Andreas Weiermann)
The zoom link can be found via the following link:
https://www.proofsociety.org/proof-theory-seminar/
The talk will be recorded.
Best,
Andreas Weiermann
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