Abstract
We use hyperbolic towers to answer some model-theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the generic type p0 but that there is a finitely generated model which omits p(2)0. We exhibit a finitely generated model in which there are two maximal independent sets of realizations of the generic type which have different cardinalities. We also show that a free product of homogeneous groups is not necessarily homogeneous.
Original language | English |
---|---|
Pages (from-to) | 521-539 |
Number of pages | 19 |
Journal | Notre Dame Journal of Formal Logic |
Volume | 54 |
Issue number | 3-4 |
DOIs | |
State | Published - 2013 |
Externally published | Yes |
Keywords
- Free group
- Generic type
- Homogeneity
- Hyperbolic towers
- Stable groups
All Science Journal Classification (ASJC) codes
- Logic