The main subjects of the course are provability, definability, decidability, and the strong connections between them. Among other things, we shall present Goedel's  theorems on the limitations of formal proofs, Tarski's  theorem on the undefinability of the concept of mathematical truth, and Church Theorem about the undecidability of Arithmetics and other branches of Mathematics. The presentation will include precise formulations of the theorems, description of the main ideas of their proofs, followed by their full details, and discussions of the implication of the theorems to Mathematics, Computer science, and Philosophy.

The course will be given this year in English.