Imaginaries in dense pairs of real-closed fields
| dc.contributor.advisor | Boxall, Gareth John | en_ZA |
| dc.contributor.author | Rakotonarivo, Tsinjo Odilon | en_ZA |
| dc.contributor.other | Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences | en_ZA |
| dc.date.accessioned | 2017-02-20T18:54:01Z | |
| dc.date.accessioned | 2017-03-29T12:18:20Z | |
| dc.date.available | 2017-02-20T18:54:01Z | |
| dc.date.available | 2017-03-29T12:18:20Z | |
| dc.date.issued | 2017-03 | |
| dc.description.abstract | 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) | en_ZA |
| dc.description.abstract | 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) | af_ZA |
| dc.format.extent | vii, 40 pages | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/10019.1/101187 | |
| dc.language.iso | en_ZA | en_ZA |
| dc.publisher | Stellenbosch : Stellenbosch University | en_ZA |
| dc.rights.holder | Stellenbosch University | en_ZA |
| dc.subject | Imaginaries (Mathematics) | en_ZA |
| dc.subject | Dense pairs (Mathematics) | en_ZA |
| dc.subject | Real-closed fields (Mathematics) | en_ZA |
| dc.subject | Completeness (Mathematics) | en_ZA |
| dc.subject | Quantifier elimination (Mathematics) | en_ZA |
| dc.subject | UCTD | en_ZA |
| dc.subject | Model theory (Mathematics) | en_ZA |
| dc.title | Imaginaries in dense pairs of real-closed fields | en_ZA |
| dc.type | Thesis | en_ZA |