{"id":16372,"date":"2002-12-04T00:00:00","date_gmt":"2002-12-04T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/projective-forcing-forcing-projectiu\/"},"modified":"2002-12-04T00:00:00","modified_gmt":"2002-12-04T00:00:00","slug":"projective-forcing-forcing-projectiu","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/projective-forcing-forcing-projectiu\/","title":{"rendered":"Projective forcing\/ forcing projectiu"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Roger Bosch Bastardas <\/strong><\/h2>\n<p>En esta tesis se estudian los \u00f3rdenes parciales proyectivos; esto es, los \u00f3rdenes parciales en el plano real que son definibles mediante f\u00f3rmulas cuyos cuantificadores var\u00edan s\u00f3lo sobre n\u00fameros reales y n\u00fameros naturales. estudiamos estos \u00f3rdenes parciales como nociones de forcing.  el primer cap\u00edtulo est\u00e1 dedicado a demostrar que el axioma de martin para \u00f3rdenes parciales proyectivos (ma(proj)) es m\u00e1s debil que el axioma de martin (ma). Para ello se define una noci\u00f3n de forcing que permite obtener modelos de ma(proj) y la negaci\u00f3n de la hipotesis del continuo. Seguidamente, usando esta noci\u00f3n de forcing, se demuestra, partiendo de un modelo de zfc con un cardinal d\u00e9bilmente compacto, que hay modelos de zfc m\u00e1s ma(proj) y la negaci\u00f3n de la hip\u00f3tesis del continuo, en los que hay estructuras no numerables cuya existencia est\u00e1 prohibida por ma. Finalmente, se demuestra que en cieertos casos se puede prescindir del cardinal d\u00e9bilmente compacto.  en el segundo cap\u00edtulo se estudian las propiedades de absolutidad gen\u00e9rica entre un modelo de la teor\u00eda de conjuntos y sus extensiones gen\u00e9ricas. en primer lugar se estudian los modelos de solovay, la clase de todos los conjuntos construibles a partir de todos los reales del modelo resultante de colapsar un cardinal inaccesible. Tambi\u00e9n se estudian algunas consecuencias de las propiedades de absolutidad gen\u00e9rica. El resto del segundo cap\u00edtulo est\u00e1 dedicado a la demostraci\u00f3n de una serie de resultados de equiconsistencia entre las propiedades de absolutidad gen\u00e9rica para ciertas clases de \u00f3rdenes parciales y la existencia de grandes cardinales mahlo-definibles, y se demuestra que, m\u00f3dulo zfc, son equiconsistentes: 1)la existencia de estos nuevos cardinales; 2) la existencia de un modelo de zfc para el cual todas las f\u00f3rmulas del lenguaje de la teor\u00eda de conjuntos con par\u00e1metros ordinales y reales en el modelo son absolutas el modelo y cualquiera de sus extensiones ge<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Projective forcing\/ forcing projectiu<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Projective forcing\/ forcing projectiu <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Roger Bosch Bastardas <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 12\/04\/2002<\/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>Joan Bagaria Pigrau<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Carlos Martinez alonso <\/li>\n<li>peter Keople (vocal)<\/li>\n<li>thomas Jech (vocal)<\/li>\n<li>pilar Dellunde clave (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Roger Bosch Bastardas En esta tesis se estudian los \u00f3rdenes parciales proyectivos; esto es, los \u00f3rdenes parciales [&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 center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[2809,951,3747,3748,10816,126,51790],"tags":[10821,19012,51792,33758,51791,51793],"class_list":["post-16372","post","type-post","status-publish","format-standard","hentry","category-algebra","category-barcelona","category-logica","category-logica-deductiva","category-logica-matematica","category-matematicas","category-teoria-axiomatica-de-conjuntos","tag-carlos-Martinez-alonso","tag-joan-bagaria-pigrau","tag-peter-keople","tag-pilar-dellunde-clave","tag-roger-bosch-bastardas","tag-thomas-jech"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/16372","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=16372"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/16372\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=16372"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=16372"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=16372"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}