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Logic Journal of IGPL Advance Access originally published online on October 17, 2007
Logic Journal of IGPL 2007 15(5-6):637-651; doi:10.1093/jigpal/jzm043
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

On Extensions of Elementary Submodels by Forcing*

Lúcia R. Junqueira

Universidade de São Paulo, São Paulo, Brazil. E-mail: lucia{at}ime.usp.br

Paul Larson

Miami University, Oxford, Ohio, USA. E-mail: larsonpb{at}muohio.edu

Marcelo D. Passos

Universidade de São Paulo, São Paulo, Brazil. E-mail: md_passos{at}yahoo.com


  Abstract

We study when a partial order Formula preserves certain properties of an elementary submodel (of a structure of the form H{theta}), including countable closure and {omega}-covering. In particular, we discuss the existence of {omega}-covering elementary submodels of different sizes.

Key Words: forcing • elementary submodels • {omega}-covering.

*Dedicated to the memory of Prof. Edison Farah


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