"Babes-Bolyai" University of Cluj-Napoca
Faculty of Mathematics and Computer Science

Selected topics of logical mathematics
Code
Semes-
ter
Hours: C+S+L
Credits
Type
Section
MA014
8
2+2+0
10
optional
Informatică
MA014
8
2+2+0
10
optional
Matematica Economica
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.