Equational Logic
DOI:
https://doi.org/10.24867/15JV01CrvenkovicKeywords:
Equational relation, equational classes of algebras, Tarski’s problem, incompleatness theorem.Abstract
Basic notions and theorems of first order logic and equational logic are given. Some examples of equational classes og algebras are presented. The main model is Formal number theory, given by Peano axioms. The special part is devoted to Tarski's High School problem, and elementary part of the proof is presented. Also, the short proof of incompletness theorem of K. Gödel is given.
References
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[2] R. Gurevič, Equational theory of positive numbers with exponantiation is not finitely axiomatizable, annals of Pure and Applied Logic 49, 1-30, 1990.
[3] R. Dedekind, Was sind und was sallen die Zahlen, Vierweg, 1898. [2] A.E. Bryson, Y.C. Ho, “Applied Optimal Control”, New York, Wiley, 1975.
[4] J. Doned, A. Tarski, An extended arithmetic of ordinal numbers, Fundamenta Mathematice, 65, 95-127, 1969.
[5] A. I. Wilkie, On exponentiation - a solution to Tarski's high school problem, Oxford University 1980.
[6] S. Burris, S. Lee, Tarski's high school identities, American Mathematical Monthly, 100, No. 3, 231-236, 1993.
[7] S. Burris, S. Lee, Small models of the high school identities, International Journal of Algebra and Computation, Vol. 2., No. 2. 139-178, 1992.
[8] S. Burris, K. Yeats, The Saga of the High School Identities, Algebra Universalis, Vol. 52, 325-342, 2008.
[9] J. Tassarotti, Formalization of Tarski's High School Algebra Problem in Coq. GitHub https://github.com/jtassarotti/tarski-hsap, 2015.
[2] R. Gurevič, Equational theory of positive numbers with exponantiation is not finitely axiomatizable, annals of Pure and Applied Logic 49, 1-30, 1990.
[3] R. Dedekind, Was sind und was sallen die Zahlen, Vierweg, 1898. [2] A.E. Bryson, Y.C. Ho, “Applied Optimal Control”, New York, Wiley, 1975.
[4] J. Doned, A. Tarski, An extended arithmetic of ordinal numbers, Fundamenta Mathematice, 65, 95-127, 1969.
[5] A. I. Wilkie, On exponentiation - a solution to Tarski's high school problem, Oxford University 1980.
[6] S. Burris, S. Lee, Tarski's high school identities, American Mathematical Monthly, 100, No. 3, 231-236, 1993.
[7] S. Burris, S. Lee, Small models of the high school identities, International Journal of Algebra and Computation, Vol. 2., No. 2. 139-178, 1992.
[8] S. Burris, K. Yeats, The Saga of the High School Identities, Algebra Universalis, Vol. 52, 325-342, 2008.
[9] J. Tassarotti, Formalization of Tarski's High School Algebra Problem in Coq. GitHub https://github.com/jtassarotti/tarski-hsap, 2015.
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Published
2021-12-09
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Section
Mathematics in Engineering
