4 papers
Untranscendable order types
Garrett Ervin, Alberto Marcone, Thilo Weinert
We introduce and study a multiplicative analogue of additive indecomposability for linear order types that we call untranscendability, as well as a strengthening that we call -u…
Reverse mathematics and dimension of posets
Alberto Marcone, Andrea Volpi
Order dimension theory measures the complexity of partially ordered sets by quantifying how far they are from being linearly ordered. In this paper we study classical bounding resu…
Chains and antichains in the Weihrauch lattice
Steffen Lempp, Alberto Marcone, Manlio Valenti
We study the existence and the distribution of "long" chains in the Weihrauch degrees, mostly focusing on chains with uncountable cofinality. We characterize when such chains have…
A jump operator on the Weihrauch degrees
Uri Andrews, Steffen Lempp, Alberto Marcone +2
A partial order admits a jump operator if there is a map that is strictly increasing and weakly monotone. Despite its name, the jump in the Weihrauch la…