8 papers · 1 filter
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…
The strength of compactness for countable complete linear orders
Paul Shafer
We investigate the statement "the order topology of every countable complete linear order is compact" in the framework of reverse mathematics, and we find that the statement's stre…
Ekeland's variational principle in weak and strong systems of arithmetic
David Fernández-Duque, Paul Shafer, Keita Yokoyama
We analyze Ekeland's variational principle in the context of reverse mathematics. We find that that the full variational principle is equivalent to -, a strong t…
Cohesive Powers of Linear Orders
Rumen Dimitrov, Valentina Harizanov, Andrey Morozov +3
Cohesive powers of computable structures can be viewed as effective ultraproducts over effectively indecomposable sets called cohesive sets. We investigate the isomorphism types of…
Randomness notions and reverse mathematics
André Nies, Paul Shafer
We investigate the strength of a randomness notion as a set-existence principle in second-order arithmetic: for each there is an that is -random re…
Comparing the degrees of enumerability and the closed Medvedev degrees
Paul Shafer, Andrea Sorbi
We compare the degrees of enumerability and the closed Medvedev degrees and find that many situations occur. There are nonzero closed degrees that do not bound nonzero degrees of e…