Modern Logic

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

Algebraic equivalents of Kurepa's Hypotheses

R. M. Dimitrić

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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

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

First available in Project Euclid: 13 April 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


Dimitrić, R. M. Algebraic equivalents of Kurepa's Hypotheses. Mod. Log. 8 (2000), no. 1-2, 28--46.

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