More on bases of uncountable free abelian groups

Abstract

We extend results found by Greenberg, Turetsky, and Westrick in [7] and investigate effective properties of bases of uncountable free abelian groups. Assuming V = L, we show that if κ is a regular uncountable cardinal and X is a ∆11(Lκ) subset of κ, then there is a κ-computable free abelian group whose bases cannot be effectively computed by X. Unlike in [7], we give a direct construction.

On the Definability and Complexity of Sets and Structures

“…In chapter 4, we prove a novel result concerning the complexity of bases of uncountable free abelian groups, obtained in collaboration with Noam Greenberg, Saharon Shelah, and Daniel Turetsky. The paper upon which our results are based has been accepted for publication [55]; our work is principally structural instead of algebraic.…”