Year: 2017
Type: preprint
Abstract: In this short note, using results of Bourgain, Fremlin, and Talagrand \cite{BFT}, we show that for a countable structure $M$, a saturated elementary extension $M^*$ of $M$ and a formula $ϕ(x,y)$ the following are equivalent: (i) $ϕ(x,y)$ is NIP on $M$ (in the sense of Definition 2.1). (ii) Whenever $p(x)\in S_ϕ(M^*)$ is finitely satisfiable in $M$ then it is Baire 1 definable over $M$ (in sense of Definition 2.5).
Source: arXiv (Cornell University)
Author: Khanaki, Karim
Institution: Arak University of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2617680063