PP-2015-20: Possible Worlds Semantics for Classical Logic

PP-2015-20: van Benthem, Johan (2015) Possible Worlds Semantics for Classical Logic. [Report]

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Abstract

Classical logic can be given a semantics based on models consisting of partial information stages, much like those for intuitionistic logic. In this way, a completeness proof becomes much more perspicuous. It suffices to use a unique Henkin model of consistent sets without any need for non-constructive principles about the existence of maximally consistent sets that introduce more structure than seems intuitively needed. We also show how these ideas can be extended to classical model theory, replacing ultraproducts by `filter products' allowing for a suitably modified Los Theorem. Finally, using ideas from set-theoretic forcing, we discuss how standard classical models can be generated from our stage-models by means of the method of `generic branches'.

Note:
This unpublished handwritten paper appeared as Report ZW 8018, December 1981, Mathematical Institute, Rijksuniversiteit Groningen. Some topics and results from this manuscript have been rediscovered in recent years under the heading of `possibility semantics' for classical modal and first-order logics. This recent work has a much wider range of motivations and results than what is covered here, but a version of the original source, put on-line while it is still legible, may still be of interest.

Item Type:	Report
Report Nr:	PP-2015-20
Series Name:	Prepublication (PP) Series
Year:	2015
Uncontrolled Keywords:	classical logic, intuitionistic logic, modal logic, axiom of choice, filter representation
Subjects:	Logic
Depositing User:	Johan van Benthem
Date Deposited:	12 Oct 2016 14:37
Last Modified:	12 Oct 2016 14:37
URI:	https://eprints.illc.uva.nl/id/eprint/531

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