31,301 research outputs found
Henselian valued fields and inp-minimality
We prove that every ultraproduct of -adics is inp-minimal (i.e., of burden
). More generally, we prove an Ax-Kochen type result on preservation of
inp-minimality for Henselian valued fields of equicharacteristic in the RV
language.Comment: v.2: 15 pages, minor corrections and presentation improvements;
accepted to the Journal of Symbolic Logi
Dp-minimality: basic facts and examples
We study the notion of dp-minimality, beginning by providing several
essential facts, establishing several equivalent definitions, and comparing
dp-minimality to other minimality notions. The rest of the paper is dedicated
to examples. We establish via a simple proof that any weakly o-minimal theory
is dp-minimal and then give an example of a weakly o-minimal group not obtained
by adding traces of externally definable sets. Next we give an example of a
divisible ordered Abelian group which is dp-minimal and not weakly o-minimal.
Finally we establish that the field of p-adic numbers is dp-minimal.Comment: 19 pages; simplified proof for the p-adic
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