1 results
Model theoretic connected components of finitely generated nilpotent groups
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- Journal:
- The Journal of Symbolic Logic / Volume 78 / Issue 1 / March 2013
- Published online by Cambridge University Press:
- 12 March 2014, pp. 245-259
- Print publication:
- March 2013
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- Article
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We prove that for a finitely generated infinite nilpotent group G with structure (G, ·, …), the connected component G*0 of a sufficiently saturated extension G* of G exists and equals
We construct an expansion of ℤ by a predicate (ℤ, +, P) such that the type-connected component
is strictly smaller than ℤ*0. We generalize this to finitely generated virtually solvable groups. As a corollary of our construction we obtain an optimality result for the van der Waerden theorem for finite partitions of groups.
is strictly smaller than ℤ*