Selected topics of logical mathematics |
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Teaching Staff in Charge |
Assoc.Prof. COVACI Rodica, Ph.D., rcovaci@math.ubbcluj.ro |
Aims |
Determination of the connection between the speculative and the applied aspect of mathematical logic, due to computer science. |
Content |
1. The algebra of propositions. Lyndenbaum-Tarski algebra. Boole rings and algebras.
2. n-ary bivalent functions. Normal perfect forms. 3. Deductive theories. Interpretation and model. Non-contradiction and consistency. Completeness and categoricity. Independence. 4. Logic of predicatives. Operations, quantifiers. Decision, special forms. 5. Formalized arithmetics. Godel numeration and theorems. Computability and decidability. Recursive functions and predicatives. |
References |
1. Both, N., Algebra logicii cu aplicatii, Ed. Dacia, 1984.
2. Both, N., Capitole speciale de logica matematica, Lito, 1994. 3. Novicov, P., Elemente de logica matematica, Ed. Tehn., 1966. 4. Pospelov, D., Metode logice de analiza si sinteza a schemelor (l. rusa) Moskva, 1968. 5. Vaisman, I., Fundamentele matematicii, EDP., 1968. |
Assessment |
Exam. |