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Logic Seminar

Monday, January 25, 2021
12:00pm to 1:00pm
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A method for showing Π03 -completeness
Vassilios Gregoriades, Department of Mathematics, National Technical University of Athens,

We present a method for showing that a given Π03 subset of a Polish space is in fact Π03-complete. This is motivated by some questions from V. Nestoridis about the sequential spaces ℓp and more generally about families of F-spaces (Xi)i∈(I,⪯) that form ⊆-chains, where ⪯ is a linear ordering.
The intersection ∩p>aℓp is known to be a Π03 subset of ℓq for all a,q with 0≤a<q<∞ (Nestoridis). We show that it is in fact a Π03-complete set. It turns out the proof can be generalized to the context of Polish spaces with no additional structure like linearity. This gives a method for showing Π03-completeness and in fact there are strong indications that it also gives a characterization of the latter property.

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