Full Text Available
Note: Clicking the button above will open the full text document at the original institutional repository in a new window.
Imaginaries in dense pairs of real-closed fields
ENGLISH ABSTRACT : Imaginaries are definable equivalence classes, which play an important role in model theory. In this thesis, we are interested in imaginaries of dense pairs of real-closed fields. More precisely, we consider the following problem: is acleq equal to dcleq in dense pairs of real-...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | en_ZA |
| Published: |
Stellenbosch : Stellenbosch University
2017
|
| Subjects: | |
| Tags: |
No Tags, Be the first to tag this record!
|
| _version_ | 1867614130438930432 |
|---|---|
| access_status_str | Open Access |
| author | Rakotonarivo, Tsinjo Odilon |
| author2 | Boxall, Gareth John |
| author_browse | Boxall, Gareth John Rakotonarivo, Tsinjo Odilon |
| author_facet | Boxall, Gareth John Rakotonarivo, Tsinjo Odilon |
| author_sort | Rakotonarivo, Tsinjo Odilon |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | ENGLISH ABSTRACT : Imaginaries are definable equivalence classes, which play an important
role in model theory. In this thesis, we are interested in imaginaries of
dense pairs of real-closed fields. More precisely, we consider the following
problem: is acleq equal to dcleq in dense pairs of real-closed fields?
To answer this question, we first present some results about real-closed
fields, which are basically completeness, quantifier elimination and elimination
of imaginaries. Then, we concentrate on the completeness and near
model-completeness for the theory of dense pairs of real-closed fields. And
finally, we present the key point of the thesis. Namely, we demonstrate that
acleq(∅) = dcleq(∅) but there exists A such that acleq(A) 6= dcleq(A) |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/101187 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:47:08.513Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2017 |
| publishDateRange | 2017 |
| publishDateSort | 2017 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/101187 Imaginaries in dense pairs of real-closed fields Rakotonarivo, Tsinjo Odilon Boxall, Gareth John Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences Imaginaries (Mathematics) Dense pairs (Mathematics) Real-closed fields (Mathematics) Completeness (Mathematics) Quantifier elimination (Mathematics) UCTD Model theory (Mathematics) ENGLISH ABSTRACT : Imaginaries are definable equivalence classes, which play an important role in model theory. In this thesis, we are interested in imaginaries of dense pairs of real-closed fields. More precisely, we consider the following problem: is acleq equal to dcleq in dense pairs of real-closed fields? To answer this question, we first present some results about real-closed fields, which are basically completeness, quantifier elimination and elimination of imaginaries. Then, we concentrate on the completeness and near model-completeness for the theory of dense pairs of real-closed fields. And finally, we present the key point of the thesis. Namely, we demonstrate that acleq(∅) = dcleq(∅) but there exists A such that acleq(A) 6= dcleq(A) AFRIKAANSE OPSOMMING : Imaginêres is definiëerbare ekwivalensieklasse, wat ’n belangrike rol in modelteorie speel. In hierdie tesis stel ons belang in imaginêres in dig pare van reël-geslote liggame. Meer spesifiek beskou ons die volgende probleem: is acleq gelyk aan dcleq in dig pare van reël-geslote liggame? Om hierdie vraag te beantwoord, begin ons met ’n paar resultate oor reëlgeslote liggame, namelik volledigheid, kwantoreliminasie en eliminasie van imaginêres. Daarna behandel ons die volledigheid en byna-modelvolledigheid vir die teorie van dig pare van reël-geslote liggame. Uiteindelik behandel ons die hoofresultat van hierdie tesis, d.w.s. ons bewys dat acleq(∅) = dcleq(∅) maar dat daar A bestaan sodat acleq(A) 6= dcleq(A) 2017-02-20T18:54:01Z 2017-03-29T12:18:20Z 2017-02-20T18:54:01Z 2017-03-29T12:18:20Z 2017-03 Thesis http://hdl.handle.net/10019.1/101187 en_ZA Stellenbosch University vii, 40 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Imaginaries (Mathematics) Dense pairs (Mathematics) Real-closed fields (Mathematics) Completeness (Mathematics) Quantifier elimination (Mathematics) UCTD Model theory (Mathematics) Rakotonarivo, Tsinjo Odilon Imaginaries in dense pairs of real-closed fields |
| title | Imaginaries in dense pairs of real-closed fields |
| title_full | Imaginaries in dense pairs of real-closed fields |
| title_fullStr | Imaginaries in dense pairs of real-closed fields |
| title_full_unstemmed | Imaginaries in dense pairs of real-closed fields |
| title_short | Imaginaries in dense pairs of real-closed fields |
| title_sort | imaginaries in dense pairs of real closed fields |
| topic | Imaginaries (Mathematics) Dense pairs (Mathematics) Real-closed fields (Mathematics) Completeness (Mathematics) Quantifier elimination (Mathematics) UCTD Model theory (Mathematics) |
| url | http://hdl.handle.net/10019.1/101187 |
| work_keys_str_mv | AT rakotonarivotsinjoodilon imaginariesindensepairsofrealclosedfields |