Generic absoluteness under projective forcing

Volume 194 / 2007

Joan Bagaria, Roger Bosch Fundamenta Mathematicae 194 (2007), 95-120 MSC: 03E15, 03E35, 03E50, 03E55. DOI: 10.4064/fm194-2-1


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 ${\mathop{\Sigma}\limits_{\textstyle\sim}}{}^1_{n+1}$.


  • Joan BagariaICREA (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
  • Roger BoschDepartamento de Filosofía
    Universidad de Oviedo
    Teniente Alfonso Martínez, s//n
    33011 Oviedo, Spain

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image