Finding bases of uncountable free Abelian groups is usually difficult

Noam Greenberg; Dan Turetsky; Linda Brown Westrick

doi:10.1090/tran/7232

Finding bases of uncountable free Abelian groups is usually difficult

Noam Greenberg
, Dan Turetsky
, Linda Brown Westrick

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We investigate effective properties of uncountable free abelian groups. We show that identifying free abelian groups and constructing bases for such groups is often computationally hard, depending on the cardinality. For example, we show, under the assumption V = L, that there is a first-order definable free abelian group with no first-order definable basis.

Original language	English (US)
Pages (from-to)	4483-4508
Number of pages	26
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	6
DOIs	https://doi.org/10.1090/tran/7232
State	Published - 2018

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/tran/7232

Cite this

@article{63c3d0277e5c4ba5800f8f52a60ab405,

title = "Finding bases of uncountable free Abelian groups is usually difficult",

abstract = "We investigate effective properties of uncountable free abelian groups. We show that identifying free abelian groups and constructing bases for such groups is often computationally hard, depending on the cardinality. For example, we show, under the assumption V = L, that there is a first-order definable free abelian group with no first-order definable basis.",

author = "Noam Greenberg and Dan Turetsky and Westrick, \{Linda Brown\}",

note = "Funding Information: Received by the editors January 23, 2016, and, in revised form, March 7, 2017. 2010 Mathematics Subject Classification. Primary 03C57; Secondary 03D60. The first author was supported by the Marsden Fund, a Rutherford Discovery Fellowship from the Royal Society of New Zealand, and by the Templeton Foundation via the Turing centenary project “Mind, Mechanism and Mathematics”. The third author was supported by the Rutherford Discovery Fellowship as a postdoctoral fellow. Publisher Copyright: {\textcopyright} 2018 American Mathematical Society.",

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T1 - Finding bases of uncountable free Abelian groups is usually difficult

AU - Greenberg, Noam

AU - Turetsky, Dan

AU - Westrick, Linda Brown

N1 - Funding Information: Received by the editors January 23, 2016, and, in revised form, March 7, 2017. 2010 Mathematics Subject Classification. Primary 03C57; Secondary 03D60. The first author was supported by the Marsden Fund, a Rutherford Discovery Fellowship from the Royal Society of New Zealand, and by the Templeton Foundation via the Turing centenary project “Mind, Mechanism and Mathematics”. The third author was supported by the Rutherford Discovery Fellowship as a postdoctoral fellow. Publisher Copyright: © 2018 American Mathematical Society.

PY - 2018

Y1 - 2018

N2 - We investigate effective properties of uncountable free abelian groups. We show that identifying free abelian groups and constructing bases for such groups is often computationally hard, depending on the cardinality. For example, we show, under the assumption V = L, that there is a first-order definable free abelian group with no first-order definable basis.

AB - We investigate effective properties of uncountable free abelian groups. We show that identifying free abelian groups and constructing bases for such groups is often computationally hard, depending on the cardinality. For example, we show, under the assumption V = L, that there is a first-order definable free abelian group with no first-order definable basis.

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UR - https://www.scopus.com/pages/publications/85044405285#tab=citedBy

U2 - 10.1090/tran/7232

DO - 10.1090/tran/7232

M3 - Article

AN - SCOPUS:85044405285

SN - 0002-9947

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EP - 4508

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 6

ER -

Finding bases of uncountable free Abelian groups is usually difficult

Abstract

All Science Journal Classification (ASJC) codes

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