Modern Logic

  • Mod. Log.
  • Volume 8, Number 1-2 (2000), 28-46.

Algebraic equivalents of Kurepa's Hypotheses

R. M. Dimitrić

Full-text: Open access

Abstract

Kurepa trees have proved to be a very useful concept with ever growing applications in diverse mathematical areas. We give a brief survey of equivalent statements in algebra, particularly in valuated vector spaces, abelian $p$-groups and non-abelian periodic groups. The survey is prefaced by an outline of the illustrious history of Kurepa's Hypothesis. An interesting aspect of the work in this area is the equivalence (via Kurepa's Hypotheses) of some statements in abelian group theory with statements in non-abelian group theory. This kind of relationship would be hard to establish, without Kurepa trees. The goal of the paper is to alert as well as familiarize the readers with this active research amalgam of set theory and algebra, but also to entice at least some to take part in the work.

Article information

Source
Mod. Log., Volume 8, Number 1-2 (2000), 28-46.

Dates
First available in Project Euclid: 13 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.rml/1081878063

Mathematical Reviews number (MathSciNet)
MR1834716

Zentralblatt MATH identifier
1021.03038

Subjects
Primary: 03E35: Consistency and independence results
Secondary: 03E05: Other combinatorial set theory 20A15: Applications of logic to group theory 20K10: Torsion groups, primary groups and generalized primary groups

Keywords
Valuated vector space Kurepa's Hypothesis abelian $p$-group $C_{\omega_1}$-group disco group discy group the Tor functor balanced projective dimension extraspecial groups FC-groups weak Kurepa Tree classes ${\cal Z}_{\kappa}$ and ${\cal Y}_{\kappa}$ Easton forcing

Citation

Dimitrić, R. M. Algebraic equivalents of Kurepa's Hypotheses. Mod. Log. 8 (2000), no. 1-2, 28--46. https://projecteuclid.org/euclid.rml/1081878063


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