Tameness in positive logic
Positive logic is a very flexible framework unifying full first-order logic with several other settings, such as Robinson’s logic (which studies existentially closed models of a possibly non-companionable first-order universal theory), hyperimaginary extensions of first-order theories (which are obtained by adding quotients by type-definable equivalence relations), and, in certain aspects, continuous logic.
The study of tameness in those contexts goes back to A. Pillay’s work on simple Robinson’s theories ([3]), and I. Ben Yaacov’s work on simple compact abstract theories ([1]). In the talk, I will present a joint work with M. Kamsma on NSOP1 in positive logic and a joint work in progress with R. Mennuni on NIP in positive logic, discussing in particular the main motivating examples for the two projects: existentially closed exponential fields (studied before by L. Haykazyan and J. Kirby in [2]) and existentially closed ordered abelian groups with an automorphism.
References
- [1]
- I. Ben Yaacov. Simplicity in compact abstract theories, Journal of Mathematical Logic, 03(02):163-191, 2003.
- [2]
- L. Haykazyan, J. Kirby, Existentially closed exponential fields, Israel Journal of Mathematics, 241(1):89-117, 2021.
- [3]
- A. Pillay. Forking in the Category of Existentially Closed Structures, Quaderni di Matematica, 6:23-42, 2000.
This document was translated from LATEX by HEVEA.