JEDNAKOSNA LOGIKA
Ključne reči:
Relacija jednakosti, jednakosne klase algebri, problem Tarskog, teorema nekompletnosti.
Apstrakt
Dati su osnovni pojmovi i teoreme logike prvog reda, kao i jednakosne logike. Navode se primeri jednakosnih klasa algebri. Osnovni model je Formalna teorija brojeva, data Peanovim aksiomama. Poseban deo rada je posvećen Srednjoškolskom problemu Tarskog i prikazan je elementaran deo dokaza. Takođe, data je skica dokaza čuvene teoreme nekompletnosti K. Gedela.
Reference
[1] P. Janičić, Matematička logika u računarstvu, Matematički fakultet, Beograd 2009.
[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.
Objavljeno
2021-12-09
Sekcija
Matematika u tehnici
