Categorical Abstract Algebraic Logic: Coordinatization is Algebraization

George Voutsadakis

Titles

Abstract

The methods of categorical abstract algebraic logic are employed to show that the classical process of the coordinatization of abstract (affine plane) geometry can be viewed under the light of the algebraization of logical systems. This link offers, on the one hand, a new perspective to the coordinatization of geometry and, on the other, enriches abstract algebraic logic by bringing under its wings a very well-known geometric process, not known hitherto to be related or amenable to its methods and techniques. The algebraization takes the form of a deductive equivalence between two institutions, one corresponding to affine plane geometry and the other to Hall ternary rings.

Keywords

Abstract Geometry, Aﬃne Plane Geometry, Coordinatization, Hall Ternary Rings, Institutions, Algebraic Institutions, Deductive Equivalence, Categorical Abstract Algebraic Logic, Interpretations, Equivalent Algebraic Semantics

References

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[15] G. Voutsadakis, Categorical Abstract Algebraic Logic: Equivalent Institutions, Studia Logica 74 (2003), pp. 275–311.

[16] G. Voutsadakis, Categorical Abstract Algebraic Logic: Algebraizable Institutions, Applied Categorical Structures 10 (2002), pp. 531–568.

Information

Information: Reports on Mathematical Logic, 2012, Number 47, pp. 125 - 145

DOI: https://doi.org/10.4467/20842589RM.12.006.0687

Article type: Original article

Titles:

Polish:

Categorical Abstract Algebraic Logic: Coordinatization is Algebraization

English:

Categorical Abstract Algebraic Logic: Coordinatization is Algebraization

Authors

George Voutsadakis

School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USA

Published at: 19.09.2023

Article status: Open

Licence: None

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George Voutsadakis (Author) - 100%

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English

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