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GENERIC EXPANSIONS OF GEOMETRIC THEORIES

Part of: Model theory

Published online by Cambridge University Press:  18 April 2024

SOMAYE JALILI ,
MASSOUD POURMAHDIAN  and
NAZANIN ROSHANDEL TAVANA
SOMAYE JALILI
Affiliation:
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE AMIRKABIR UNIVERSITY OF TECHNOLOGY (TEHRAN POLYTECHNIC) HAFEZ AVENUE 15194, P.O. BOX 15875-4413, TEHRAN, IRAN E-mail: somaye.jalili507@gmail.com, nrtavana@aut.ac.ir
MASSOUD POURMAHDIAN*
Affiliation:
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE AMIRKABIR UNIVERSITY OF TECHNOLOGY (TEHRAN POLYTECHNIC) HAFEZ AVENUE 15194, P.O. BOX 15875-4413, TEHRAN, IRAN and SCHOOL OF MATHEMATICS INSTITUTE FOR RESEARCH IN FUNDAMENTAL SCIENCES (IPM) P.O. BOX 19395-5746, TEHRAN, IRAN
NAZANIN ROSHANDEL TAVANA
Affiliation:
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE AMIRKABIR UNIVERSITY OF TECHNOLOGY (TEHRAN POLYTECHNIC) HAFEZ AVENUE 15194, P.O. BOX 15875-4413, TEHRAN, IRAN E-mail: somaye.jalili507@gmail.com, nrtavana@aut.ac.ir
*
E-mail: pourmahd@ipm.ir
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Abstract

As a continuation of ideas initiated in [19], we study bi-colored (generic) expansions of geometric theories in the style of the Fraïssé–Hrushovski construction method. Here we examine that the properties $NTP_{2}$, strongness, $NSOP_{1}$, and simplicity can be transferred to the expansions. As a consequence, while the corresponding bi-colored expansion of a red non-principal ultraproduct of p-adic fields is $NTP_{2}$, the expansion of algebraically closed fields with generic automorphism is a simple theory. Furthermore, these theories are strong with $\operatorname {\mathrm {bdn}}(\text {"}x=x\text {"})=(\aleph _0)_{-}$.

Keywords

geometric theoriesFraïssé–Hrushovski constructionbi-colored expansionsrich structuresNTP2 theoriesNSOP1 theoriessimple theories

MSC classification

Primary: 03C45: Classification theory, stability and related concepts
Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 22
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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