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Logic Journal of IGPL Advance Access originally published online on October 12, 2007
Logic Journal of IGPL 2007 15(5-6):707-739; doi:10.1093/jigpal/jzm045
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Fibred and Indexed Categories for Abstract Model Theory

Alfio Martini

Instituto de Informática – PUCRS – Brasil. E-mail: alfio{at}inf.pucrs.br

Uwe Wolter

Institute of Informatics – University of Bergen – Norway. E-mail: wolter{at}ii.uib.no

E. Hermann Haeusler

Departamento de Ciência da Computação – PUC-Rio – Brasil. E-mail: hermann{at}inf.puc-rio.br


  Abstract

Indexed and Fibred category theory have a long tradition in computer science as a language to formalize different presentations of the notion of a logic, as for instance, in the theory of institutions and general logics, and as unifying models of (categorical) logic and type theory as well. Here we introduce the notions of indexed and fibred frames and construct a rich mathematical workspace where many relevant and useful concepts of logics can be elegantly modelled. To demonstrate the applicability of these tools, essential ideas around the theory of institutions are recasted and described.

Key Words: indexed and fibred categories • Grothendieck constructions • logical systems • institutions.

Received for publication 20 September 2006.
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