Teorie dobrých uspořádání
| Thesis title in Czech: | Teorie dobrých uspořádání |
|---|---|
| Thesis title in English: | The theory of well orders |
| Key words: | teorie prvního řádu|dobré uspořádání|teorie modelů|Ehrenfeuchtovy–Fraïssého hry|eliminace kvantifikátorů|rozhodnutelnost |
| English key words: | first-order theory|well order|model theory|Ehrenfeucht–Fraïssé games|quantifier elimination|decidability |
| Academic year of topic announcement: | 2024/2025 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | Mgr. et Mgr. Emil Jeřábek, Dr., Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 08.11.2024 |
| Date of assignment: | 08.11.2024 |
| Confirmed by Study dept. on: | 11.11.2024 |
| Guidelines |
| Cílem práce je přehledně zpracovat vlastnosti prvořádové teorie dobrých uspořádání, zejm. charakterizaci k-ekvivalence a elementární ekvivalence, eliminaci kvantifikátorů, rozhodnutelnost a možnosti axiomatizace. Práce by měla být vypracována v anglickém jazyce.
The thesis should systematically develop properties of the first-order theory of well orders, esp. a characterization of k-equivalence and elementary equivalence, quantifier elimination, decidability, and variant axiom sets. The thesis should be written in English. |
| References |
| John E. Doner, Andrzej Mostowski, Alfred Tarski: The elementary theory of well-ordering – a metamathematical study, in: Logic Colloquium ’77 (A. Macintyre, L. Pacholski, J. Paris, eds.), North-Holland, 1978, pp. 1–54.
Andrzej Ehrenfeucht: An application of games to the completeness problem for formalized theories, Fundamenta Mathematicae 49 (1961), no. 2, pp. 129–141. Wilfrid Hodges: Model theory, Cambridge University Press, 1993. Joseph G. Rosenstein: Linear orderings, Academic Press, New York, 1982. Robert Vaught: On the work of Andrzej Ehrenfeucht in model theory, in: Structures in logic and computer science: A selection of essays in honor of A. Ehrenfeucht (J. Mycielski, G. Rozenberg, A. Salomaa, eds.), vol. 1261 of Lecture Notes in Computer Science, Springer, 1997. |