Split Principles

2017/02/22 by Günter Fuchs, Fuchs, Gunter, Kaethe Minden +1
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1702.07041

Abstract

We introduce the split principles and show that they bear tight connections to large cardinal properties such as inaccessibility, weak compactness, subtlety, almost ineffability and ineffability, as well as classical combinatorial objects such as Aronszajn trees, Souslin trees or square principles. We exhibit correspondences between certain split principles and splitting numbers at uncountable cardinals.

Related

• The splitting principle and singularities
• Indiscernible extraction at small large cardinals from a higher-arity stability notion
• Some combinatorial properties of splitting trees
• Bounding, splitting, and almost disjointness
• Splitting number