More on Bases of Uncountable Free Abelian Groups

Noam Greenberg; Linus Richter; Saharon Shelah; Dan Turetsky

doi:10.1142/9789819806584_0004

More on Bases of Uncountable Free Abelian Groups

Noam Greenberg, Linus Richter, Saharon Shelah, Dan Turetsky

Einstein Institute of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

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 Δ11Lκ 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.

Original language	English
Title of host publication	Higher Recursion Theory and Set Theory
Publisher	World Scientific Publishing Co.
Pages	71-85
Number of pages	15
ISBN (Electronic)	9789819806584
ISBN (Print)	9789819806577
DOIs	https://doi.org/10.1142/9789819806584_0004
State	Published - 1 Jan 2025

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© 2025 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.

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More on Bases of Uncountable Free Abelian Groups

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