Limits of classes of finite structures in model theory
Thesis title in Czech: | Limity tříd konečných struktur v teorii modelů |
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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. |