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In this paper I will look for a first order parameterization of the theory of quandles. More specifically, I will examine one particular first order sentence to to see if it could be a first order axiomatization of Mal'cev terms in quandles. I will begin by dening first order logic, and examining some of capabilities and limitations of rst order logic. I will then explain a notion of parametrizability, explaining why certain things are parametrizable in first order and others are not. The 0-1 law for first order logic is very useful for answering questions of parametrizability, so I will explain what this law is and how it can be used (and has been used) to prove or disprove the parametrizability of a class of structures.
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Garber, Solomon, "On the First Order Axiomatization of Mal'cev Terms for Quandles" (2011). Senior Projects Fall 2011. 13.