Categorical abstract algebraic logic categorical algebraization of first-order logic without terms |
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Authors: | George Voutsadakis |
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Institution: | (1) School of Mathematics and Computer Science, Lake Superior State University, Sault Sainte Marie, MI 49783, USA |
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Abstract: | An algebraization of multi-signature first-order logic without terms is presented. Rather than following the traditional method of choosing a type of algebras and constructing an appropriate variety, as is done in the case of cylindric and polyadic algebras, a new categorical algebraization method is used: The substitutions of formulas of one signature for relation symbols in another are treated in the object language. This enables the automatic generation via an adjunction of an algebraic theory. The algebras of this theory are then used to algebraize first-order logic.Partially supported by National Science Foundation grant CCR - 9593168 |
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Keywords: | Primary: 03Gxx 18Cxx Secondary: 08Bxx 08Cxx 68N05 |
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