Geodesic
Generic absoluteness under projective forcing
Joan Bagaria 1   ; Roger Bosch 2
1 ICREA (Institució Catalana de Recerca i Estudis Avançats) and Departament de Lògica, Història i Filosofia de la Ciència Universitat de Barcelona Montalegre 6 08001 Barcelona, Spain
2 Departamento de Filosofía Universidad de Oviedo Teniente Alfonso Martínez, s//n 33011 Oviedo, Spain
Fundamenta Mathematicae, Tome 194 (2007) no. 2, pp. 95-120 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the preservation of the property of $\bf LR$ being a Solovay model under projective ccc forcing extensions. We compute the exact consistency strength of the generic absoluteness of $\bf LR$ under forcing with projective ccc partial orderings and, as an application, we build models in which Martin's Axiom holds for ${\mathop{\Sigma}\limits_{\textstyle\sim}}{}^1_n$ partial orderings, but it fails for the ${\mathop{\Sigma}\limits_{\textstyle\sim}}{}^1_{n+1}$.
DOI : 10.4064/fm194-2-1
Keywords: study preservation property being solovay model under projective ccc forcing extensions compute exact consistency strength generic absoluteness under forcing projective ccc partial orderings application build models which martins axiom holds mathop sigma limits textstyle sim partial orderings fails mathop sigma limits textstyle sim

Joan Bagaria  1   ; Roger Bosch  2

1 ICREA (Institució Catalana de Recerca i Estudis Avançats) and Departament de Lògica, Història i Filosofia de la Ciència Universitat de Barcelona Montalegre 6 08001 Barcelona, Spain
2 Departamento de Filosofía Universidad de Oviedo Teniente Alfonso Martínez, s//n 33011 Oviedo, Spain 
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Joan Bagaria; Roger Bosch. Generic absoluteness under projective forcing. Fundamenta Mathematicae, Tome 194 (2007) no. 2, pp. 95-120. doi: 10.4064/fm194-2-1

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