Fast growing hierarchies, ordinal collapsing and Pi^1_1-CA_0

[Andreas Weiermann]

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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