On f-generic types in Presburger Arithmetic
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Last updated：2024-02-21
Studies in Logic, Vol. 12, No. 3 (2019): 57–78 PII: 1674-3202(2019)-03-0057-22
Ningyuan Yao
Abstract. We study the f-generics of ordered additive group G of any model of Presburger Arithmetic, and give a classification for the f-generic types of 
for any 
. As an application of this classification theorem, we conclude that every f-generic type of 
is ∅- definable. We also consider the multiplicative group H of the p-adic field Qp, and prove that every f-generic type of 
is also ∅-definable.