JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Fundamenta Mathematicae

Artykuły w formacie PDF dostępne są dla subskrybentów, którzy zapłacili za dostęp online, po podpisaniu licencji Licencja użytkownika instytucjonalnego. Czasopisma do 2009 są ogólnodostępne (bezpłatnie).

## Pairs of theories satisfying a Mordell–Lang condition

### Tom 251 / 2020

Fundamenta Mathematicae 251 (2020), 131-160 MSC: Primary 03C10; Secondary 03C64. DOI: 10.4064/fm857-1-2020 Opublikowany online: 1 April 2020

#### Streszczenie

This paper proposes a new setup for studying pairs of structures. This new framework includes many of the previously studied classes of pairs, such as dense pairs of o-minimal structures, lovely pairs, fields with Mann groups, and $H$-structures, but also includes new ones, such as pairs consisting of a real closed field and a pseudo real closed subfield, and pairs of vector spaces with different fields of scalars. We use the larger generality of this framework to answer, at least in part, a couple concrete open questions raised about open cores and decidability. The first is: for which subfields $K \subseteq \mathbb R$ is $\mathbb R$ as an ordered $K$-vector space expanded by a predicate for $\mathbb Q$ decidable? The second is whether there is a subfield $K$ of a real closed field that is not real closed, yet every open set definable in the expansion of the real field by $K$ is semialgebraic.

#### Autorzy

• Alexi Block GormanDepartment of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801, U.S.A.
e-mail
• Philipp HieronymiDepartment of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801, U.S.A.
e-mail
• Elliot KaplanDepartment of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801, U.S.A.
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek