2000 character limit reached
Universal Algebra and Mathematical Logic (1104.4606v1)
Published 24 Apr 2011 in math.LO, cs.FL, and cs.LO
Abstract: 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.