Limits of classes of finite structures in model theory

• Thesis title in Czech: Limity tříd konečných struktur v teorii modelů
• Thesis title in English: Limits of classes of finite structures in model theory
• Key words: limita, diskrétní lineární uspořádání, Fraïssého amalgamace, forcing, konečná struktura, teorie modelů
• English key words: limit, discrete linear orders, Fraïssé's amalgamation, forcing, finite structure, model theory
• Academic year of topic announcement: 2016/2017
• Thesis type: diploma thesis
• Thesis language: angličtina
• Department: Department of Algebra (32-KA)
• Supervisor: prof. RNDr. Jan Krajíček, DrSc.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 22.02.2017
• Date of assignment: 23.02.2017
• Confirmed by Study dept. on: 21.03.2017
• Date and time of defence: 12.09.2019 10:00
• Date of electronic submission: 19.07.2019
• Date of submission of printed version: 19.07.2019
• Date of proceeded defence: 12.09.2019
• Opponents: doc. Mgr. Jan Šaroch, Ph.D.

Guidelines

Model theory knows several constructions of infinite
structures that can be interpreted as limits of classes
of finite structures (e.g. ultraproduct, compactness
arguments, non-standard analysis, asymptotic classes,
pseudofinite structures, robust classes, etc.). The aim
of the Thesis will be to compare these constructions
on specific examples.

References

Dugald Macpherson and Charles Steinhorn, De�finability in
classes of �finite structures, in: Javier Esparza, C. Michaux,
and C. Steinhorn, editors, Finite and Algorithmic
Model Theory, London Mathematical Society Lecture Note
Series (No. 379), pages 140–176. Cambridge University Press, 2011.
http://ambio1.leeds.ac.uk/Pure/staff/macpherson/macphersonsteinhorn.pdf

Jaroslav Nesetril and Patrice Ossona De Mendez, A Model Theory
Approach to Structural Limits,
Commentationes Mathematicae Universitatis Carolinae 53, 4 (2012) 581-603.
http://arxiv.org/abs/1303.2865

J. Väänänen, Pseudo-finite model theory, Matematica Contemporanea,
vol 24, 2003, pp.169-183.
http://www.math.helsinki.fi/logic/people/jouko.vaananen/qf_final.pdf

Preliminary scope of work

Limity tříd konečných struktur v teorii modelů.

Preliminary scope of work in English

Limits of classes of finite structures in model theory.