{"id":24561,"date":"2003-10-07T00:00:00","date_gmt":"2003-10-07T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/extensiones-de-fragmentos-de-la-aritmetica\/"},"modified":"2003-10-07T00:00:00","modified_gmt":"2003-10-07T00:00:00","slug":"extensiones-de-fragmentos-de-la-aritmetica","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/sevilla\/extensiones-de-fragmentos-de-la-aritmetica\/","title":{"rendered":"Extensiones de fragmentos de la aritm\u00e9tica"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Andres Cord\u00f3n Franco <\/strong><\/h2>\n<p>El presente trabajo se enmarca dentro del campo de estudio de los modelos de la aritm\u00e9tica de peano: pa. En l\u00edneas generales, se desarrolla un estudios sistem\u00e1tico de fragmentos de la aritm\u00e9tica empleando como metodolog\u00eda el an\u00e1lisis de la complejidad de sus extensiones. Para medir la complejidad de una extensi\u00f3n, se consideran dos criterios:  (&#8211;) la complejidad sint\u00e1ctica de sus axiomas.  (&#8211;) la complejidad descriptiva, desde el punto de vista computacional, del conjunto de sus axiomas.  en la primera parte del trabajo, refinamos propiedades conocidas sobre estructuras de elemenos definibles, prestando especial atenci\u00f3n a aquellos resultados que establecen que en dichas estructuras no son v\u00e1lidos esquemas de inducci\u00f3n o colecci\u00f3n. Estos  refinamientos son esenciales para obtener propiedades \u00f3ptimas sobre existencia de extensiones de fragmentos de una cierta complejidad.  en la parte central del trabajo, se obtienen resultados (en muchos casos \u00f3ptimos) sobre la complejidad sint\u00e1ctica y descriptiva de extensiones de framentos. Cl\u00e1sicos de la aritm\u00e9tica (esto es, los obtenidos al restringir los principios de inducci\u00f3n, colecci\u00f3n o minimizaci\u00f3n a f\u00f3rmulas $sigma-n$ o $pi-n$).  en la tercera parte del trabajo, se emplean los resultados sobre extensiones anteriores para estudiar fragmentos relativizados, es decir, los fragmentos de la aritm\u00e9tica obtenidos al restringir los principios de inducci\u00f3n, colecci\u00f3n, o minimizaci\u00f3n a f\u00f3rmulas $delta-n(t)$ (esto es, f\u00f3rmulas $sigma-n$ equivalentes a una f\u00f3rmula $pi-n$ y tales que la teor\u00eda t demuestra dicha equiValencia). dichos esquemas hab\u00edan sido considerados previamente por fern\u00e1ndez margarit y lara mart\u00edn en relaci\u00f3n al estudio del problema de jeff paris sobre la equiValencia de los fragmentos de inducci\u00f3n y minimizaci\u00f3n para f\u00f3rmulas $delta-n$. Una de las aportaciones m\u00e1s novedosas del presente trabajo es que se proporciona una nueva metodolog\u00eda p<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Extensiones de fragmentos de la aritm\u00e9tica<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Extensiones de fragmentos de la aritm\u00e9tica <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Andres Cord\u00f3n Franco <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Sevilla<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 10\/07\/2003<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Alejandro Fern\u00e1ndez Margarit<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Carlos Martinez alonso <\/li>\n<li>margarita Otero dom\u00ednguez (vocal)<\/li>\n<li>enrique Casanovas ruiz-fornells (vocal)<\/li>\n<li>Rafael Farre cirera (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Andres Cord\u00f3n Franco El presente trabajo se enmarca dentro del campo de estudio de los modelos de [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center 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