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On the generic type of the free group
Journal of Symbolic Logic 76 (1):227 - 234 (2011)
Abstract
We answer a question raised in [9], that is whether the infinite weight of the generic type of the free group is witnessed in F ω . We also prove that the set of primitive elements in finite rank free groups is not uniformly definable. As a corollary, we observe that the generic type over the empty set is not isolated. Finally, we show that uncountable free groups are not N₁-homogeneousLinks
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Citations of this work
On Superstable Expansions of Free Abelian Groups.Daniel Palacín & Rizos Sklinos - 2018 - Notre Dame Journal of Formal Logic 59 (2):157-169.
On the (non) superstable part of the free group.Chloé Perin & Rizos Sklinos - 2016 - Mathematical Logic Quarterly 62 (1-2):88-93.
Hyperbolic Towers and Independent Generic Sets in the Theory of Free Groups.Larsen Louder, Chloé Perin & Rizos Sklinos - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):521-539.
Homogeneity in relatively free groups.Oleg Belegradek - 2012 - Archive for Mathematical Logic 51 (7-8):781-787.
Two remarks on elementary theories of groups obtained by free constructions.Eric Jaligot - 2013 - Mathematical Logic Quarterly 59 (1-2):12-18.
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