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The definable (p,q)-theorem for dense pairs of certain geometric structures
Thesis (PhD)--Stellenbosch University, 2021.
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| Format: | Thesis |
| Language: | en_ZA |
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Stellenbosch : Stellenbosch University
2021
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| _version_ | 1867613753968689152 |
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| 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 | Thesis (PhD)--Stellenbosch University, 2021. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/123797 |
| institution | Stellenbosch University (South Africa) |
| language | en_ZA |
| last_indexed | 2026-06-10T12:41:09.576Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/123797 The definable (p,q)-theorem for dense pairs of certain geometric structures Rakotonarivo, Tsinjo Odilon Boxall, Gareth John Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Mathematics. (p,q)-theorem Dense pairs Geometric structures Prediction (Logic) Combinatorial analysis Finite geometries UCTD Thesis (PhD)--Stellenbosch University, 2021. ENGLISH ABSTRACT: The definable (p, q)-conjecture is a model-theoretic version of a (p, q)- theorem in combinatorics, which was expressed in the form of a question by A. Chernikov and P. Simon in 2015. Researchers have proved that the property holds for certain classes of structures. Based on those existing results, the main objective of the present thesis is to show that the definable (p, q)-conjecture holds for a dense pair of geometric distal structures that satisfies the following condition: algebraic closure and definable closure are the same in sense of the original geometric structure. Independently, we also explore a different approach to prove that under some conditions, the definable (p, q)-conjecture holds in certain cases for dense pairs of real closed ordered fields. AFRIKAANSE OPSOMMING: Die definieerbare (p, q)-vermoede is ’n model-teoretiese weergawe van ’n (p, q)-stelling in kombinatorika, wat in 2015 deur A. Chernikov en P. Simon in die vorm van ’n vraag uitgedruk is. Navorsers het bewys dat die eienskap vir seker klasse van strukture geldig is. Op grond van daardie bestaande resultate is die hoofdoel van hierdie tesis om aan te toon dat die definieerbare (p, q)-vermoede geldig is vir ’n digte paar meetkundige distale strukture wat die volgende voorwaarde bevredig: algebraïese afsluiting en definieerbare afsluiting is dieselfde in die sin van die oorspronklike meetkundige struktuur. Onafhanklik hiervan ondersoek ons ’n ander benadering om te bewys dat, onder seker voorwaardes, die definieerbare (p, q)-vermoede geldig is vir seker gevalle vir digte pare van reële geslote geordende liggame. Doctoral 2021-11-21T09:16:45Z 2021-12-22T14:21:58Z 2021-11-21T09:16:45Z 2021-12-22T14:21:58Z 2021-12 Thesis http://hdl.handle.net/10019.1/123797 en_ZA Stellenbosch University x, 66 pages application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | (p,q)-theorem Dense pairs Geometric structures Prediction (Logic) Combinatorial analysis Finite geometries UCTD Rakotonarivo, Tsinjo Odilon The definable (p,q)-theorem for dense pairs of certain geometric structures |
| title | The definable (p,q)-theorem for dense pairs of certain geometric structures |
| title_full | The definable (p,q)-theorem for dense pairs of certain geometric structures |
| title_fullStr | The definable (p,q)-theorem for dense pairs of certain geometric structures |
| title_full_unstemmed | The definable (p,q)-theorem for dense pairs of certain geometric structures |
| title_short | The definable (p,q)-theorem for dense pairs of certain geometric structures |
| title_sort | definable p q theorem for dense pairs of certain geometric structures |
| topic | (p,q)-theorem Dense pairs Geometric structures Prediction (Logic) Combinatorial analysis Finite geometries UCTD |
| url | http://hdl.handle.net/10019.1/123797 |
| work_keys_str_mv | AT rakotonarivotsinjoodilon thedefinablepqtheoremfordensepairsofcertaingeometricstructures AT rakotonarivotsinjoodilon definablepqtheoremfordensepairsofcertaingeometricstructures |