  In this paper, first-order logic is interpreted in the framework of universal
algebra, using the clone theory developed in three previous papers. We first
define the free clone T(L, C) of terms of a first order language L over a set C
of parameters in a standard way. The free right algebra F(L, C) of formulas
over T(L, C) is then generated by atomic formulas. Structures for L over C are
represented as perfect valuations of F(L, C), and theories of L are represented
as filters of F(L). Finally Godel's completeness theorem and first
incompleteness theorem are stated as expected.
