Categorical Abstract Algebraic Logic: Coordinatization is Algebraization
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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.
07 - 07 - 2015
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