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math.LO2020
Ordinal analysis of partial combinatory algebras
Paul Shafer, Sebastiaan A. Terwijn
For every partial combinatory algebra (pca), we define a hierarchy of extensionality relations using ordinals. We investigate the closure ordinals of pca's, i.e. the smallest ordin…
math.LO2020
On cohesive powers of linear orders
Rumen Dimitrov, Valentina Harizanov, Andrey Morozov +3
Cohesive powers of computable structures are effective analogs of ultrapowers, where cohesive sets play the role of ultrafilters. Let , , and denote the respective order-…
math.LO2020
An inside/outside Ramsey theorem and recursion theory
Marta Fiori-Carones, Paul Shafer, Giovanni Soldà
Inspired by Ramsey's theorem for pairs, Rival and Sands proved what we refer to as an inside/outside Ramsey theorem: every infinite graph contains an infinite subset such t…