Partial Model Theory as Model Theory

Citation data:

Ergo, an Open Access Journal of Philosophy, ISSN: 2330-4014, Vol: 2, Issue: 20171113, Page: 563-580

Publication Year:
2015
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Repository URL:
http://philsci-archive.pitt.edu/id/eprint/11710
DOI:
10.3998/ergo.12405314.0002.022
Author(s):
Lutz, Sebastian
Publisher(s):
University of Michigan Library, Michigan Publishing, Michigan Publishing, University of Michigan Library
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article description
I show that the partial truth of a sentence in a partial structure is equivalent to the truth of that sentence in an expansion of a structure that corresponds naturally to the partial structure. Further, a mapping is a partial homomorphism/partial isomorphism between two partial structures if and only if it is a homomorphism/isomorphism between their corresponding structures. It is a corollary that the partial truth of a sentence in a partial structure is equivalent to the truth of a specific Ramsey sentence in a corresponding structure. Hence the partial structures approach can be expressed in standard first or second-order model theory, and it can be captured in the received view on scientific theories as developed by Carnap and Hempel.

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