On genericity and weight in the free group
Anand Pillay
TL;DR
This paper proves that the generic type in free nonabelian groups has infinite weight, indicating a high level of complexity and strengthening the understanding of the group's model-theoretic properties.
Contribution
It establishes that the generic type in free nonabelian groups has infinite weight, advancing the theoretical understanding of their model-theoretic structure.
Findings
The generic type in free nonabelian groups has infinite weight.
This result strengthens the non-superstability of free groups.
Abstract
I prove that the generic type of the free nonabelian group has infinite weight (strengthening non superstability of the free group).
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Taxonomy
TopicsAdvanced Topology and Set Theory · advanced mathematical theories · Geometric and Algebraic Topology