A Co-free Construction for Elementary Doctrines

We provide a construction which co-freely adds elementary structure to a primary doctrine in the sense of Lawvere. We show that the construction preserves all the first order logical structures that the starting doctrine may have. Moreover it forces the Principle of Propositional Extensionality when...

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Veröffentlicht in:	Applied categorical structures 2015-02, Vol.23 (1), p.29-41
1. Verfasser:	Pasquali, Fabio
Format:	Artikel
Sprache:	eng
Schlagworte:	Convex and Discrete Geometry Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Theory of Computation
Online-Zugang:	Volltext
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Zusammenfassung:	We provide a construction which co-freely adds elementary structure to a primary doctrine in the sense of Lawvere. We show that the construction preserves all the first order logical structures that the starting doctrine may have. Moreover it forces the Principle of Propositional Extensionality when applied to triposes.
ISSN:	0927-2852 1572-9095
DOI:	10.1007/s10485-013-9358-z