Zobrazeno 1 - 10
of 282
pro vyhledávání: '"Johnson Will"'
We classify dp-minimal integral domains, building off the existing classification of dp-minimal fields and dp-minimal valuation rings. We show that if R is a dp-minimal integral domain, then R is a field or a valuation ring or arises from the followi
Externí odkaz:
http://arxiv.org/abs/2405.21014
Autor:
Johnson, Will
We prove generic differentiability in $P$-minimal theories, strengthening an earlier result of Kuijpers and Leenknegt. Using this, we prove Onshuus and Pillay's $P$-minimal analogue of Pillay's conjectures on o-minimal groups. Specifically, let $G$ b
Externí odkaz:
http://arxiv.org/abs/2404.17234
Autor:
Johnson, Will
Let $T$ be a theory with a definable topology. $T$ is t-minimal in the sense of Mathews if every definable set in one variable has finite boundary. If $T$ is t-minimal, we show that there is a good dimension theory for definable sets, satisfying prop
Externí odkaz:
http://arxiv.org/abs/2404.11453
Autor:
Johnson, Will
We show that C-minimal fields (i.e., C-minimal expansions of ACVF) have the exchange property, answering a question of Haskell and Macpherson. Additionally, we strengthen some theorems of Cubides Kovacsics and Delon on C-minimal fields. First, we sho
Externí odkaz:
http://arxiv.org/abs/2403.17478
Autor:
Johnson, Will, Yao, Ningyuan
We generalize two of our previous results on abelian definable groups in $p$-adically closed fields to the non-abelian case. First, we show that if $G$ is a definable group that is not definably compact, then $G$ has a one-dimensional definable subgr
Externí odkaz:
http://arxiv.org/abs/2308.01527
Autor:
Johnson, Will, Ye, Jinhe
If $C$ is a curve over $\mathbb{Q}$ with genus at least $2$ and $C(\mathbb{Q})$ is empty, then the class of fields $K$ of characteristic 0 such that $C(K) = \varnothing$ has a model companion, which we call $C\mathrm{XF}$. The theory $C\mathrm{XF}$ i
Externí odkaz:
http://arxiv.org/abs/2303.06063
Autor:
Johnson, Will
We prove some results on NIP integral domains, especially those that are Noetherian or have finite dp-rank. If $R$ is an NIP Noetherian domain that is not a field, then $R$ is a semilocal ring of Krull dimension 1, and the fraction field of $R$ has c
Externí odkaz:
http://arxiv.org/abs/2302.03315
Autor:
Guerrero, Pablo Andujar, Johnson, Will
Publikováno v:
Annals of Pure and Applied Logic 175(10): 103484 (December 2024)
We prove some technical results on definable types in $p$-adically closed fields, with consequences for definable groups and definable topological spaces. First, the code of a definable $n$-type (in the field sort) can be taken to be a real tuple (in
Externí odkaz:
http://arxiv.org/abs/2208.05815