Extensiones del problema de Büchi a distintas estructuras y potencias más altas.
| dc.contributor.advisor | Vidaux Negre, Xavier | es |
| dc.contributor.author | Pastén Vásquez, Héctor Hardy | es |
| dc.date.accessioned | 2021-05-18T23:50:18Z | |
| dc.date.accessioned | 2024-05-15T19:12:25Z | |
| dc.date.accessioned | 2024-08-28T22:32:30Z | |
| dc.date.available | 2021-05-18T23:50:18Z | |
| dc.date.available | 2024-05-15T19:12:25Z | |
| dc.date.available | 2024-08-28T22:32:30Z | |
| dc.date.issued | 2010 | |
| dc.description | Tesis para optar al grado de Magíster en Matemática | es |
| dc.description.abstract | In any commutative ring A with unit, Büchi sequences are those sequences whose second di erence of squares is the constant sequence (2). Sequences of elements xn satisfying x2 n = (x + n)2 for some xed x are Büchi sequences that we call trivial. Since we want to study sequences whose elements do not belong to certain subrings (e.g. for elds of rational functions F(z) over a eld F we are interested in sequences that are not over F) the concept of trivial sequences may vary. Büchi's Problem for a ring A asks whether there exists a positive integer M such that any Büchi sequence of length M or more is trivial. We survey the current status of knowledge for Büchi's problem and its analogues for higher-order di erences and higher powers. We propose several new and old open problems. We present a few new results and various sketches of proofs of old results (in particular : Vojta's conditional proof for the case of integers and a quite detailed proof for the case of polynomial rings in characteristic zero), and present a new and short proof of the positive answer to Büchi's problem over nite elds with p elements (originally proved by Hensley). We discuss applications to Logic (which were the initial aim for solving these problems). | es |
| dc.description.departamento | Departamento de Matemática. | es |
| dc.description.facultad | Facultad de Ciencias Físicas y Matemáticas | es |
| dc.identifier.uri | https://repositorio.udec.cl/handle/11594/5877 | |
| dc.language.iso | eng | es |
| dc.publisher | Universidad de Concepción. | es |
| dc.rights | Creative Commoms CC BY NC ND 4.0 internacional (Atribución-NoComercial-SinDerivadas 4.0 Internacional) | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/deed.es | |
| dc.source.uri | https://go.openathens.net/redirector/udec.cl?url=http://tesisencap.udec.cl/concepcion/pasten_v_h/index.html | |
| dc.subject | Campos Finitos (Álgebra) | |
| dc.subject | Ecuaciones Diferenciales | |
| dc.subject | Büchi, Problema | |
| dc.title | Extensiones del problema de Büchi a distintas estructuras y potencias más altas. | es |
| dc.type | Tesis | es |