Syllabus
- Deeper properties of classical first-order logic: arithmetization, diagonalization, formalization of proovability, strong, essential and hereditary unsolvability. Application (in set theory, arithmetics and another theories).
- Abstract logic systems. Characterizations o classical logic - Lindström theorem.
- Non-classical logic systems: second-order logic, infinitary logic (with examples), temporal logic.
A knowledge of basics of classical first-order logic is assumed.
Annotation
Mathematical logic formulates and develops the concept of deduction, truth and an algorithmic solvability. It delivers a concept of axiomatic theories and their corresponding semantic realizations called models and allows to analyze such theories with regard to consistency, completeness, decidability, descriptive complexity, to the character of axioms etc.
Moreover, it provides methods for construction of models and solves the problems of axiomatisability of classes of models. It includes beside classical two-valued logic also multi-valued, higher-order, modal, temporal and others.