Title Logic Lecture
Lecturer Péter Mekis
Codes BMA-FILD-301.1, BMA-LOTD-102.1, BMI-LOTD-102E.2, BBN-FIL-301.1
Time Friday 10:00-11:30
Venue i-109
Prerequisites The course assumes some familiarity with the basic concepts and methods of modern formal logic; most importantly, the basics of translating ordinary propositions into formulas with predicates, constants, variables, propositional connectives, and quantifiers.
Exam The course ends with an oral exam. After the last lecture, students will get the final list of the topics covered in the course. Logic masters students can pick two items of this list that they don't want to study. Other students can pick four such items. The exam will cover the rest of the topics.
Description The lectures will cover the following topics:
  1. introduction: the concept of modern formal logic and its place in the foundational studies;
  2. syntax and semantics of standard first-order languages;
  3. first-order analytic trees and the decision problem;
  4. first-order theories: basic concepts and methods;
  5. Peano arithmetic: language, definitions, basic theorems, and the standard model;
  6. standard first-order calculus: deductions and metatheorems;
  7. soundness and completeness of the standard first-order calculus;
  8. the compactness theorem and nonstandard models of Peano arithmetic;
  9. the downward Löwenheim-Skolem theorem;
  10. overview of Gödel's incompleteness results;
  11. higher-order logic;
  12. definite descriptions and semantic value gaps;
  13. modal and intensional logic.
The topics may change during the course, in accordance with student demand. The Hungarian version of the course will be easier and covers less topics.
  • Lecture notes (updated during the course)
  • Gamut, L. T. F., Logic, Language, and Meaning. Vol 1: Introduction to Logic. Chicago UP, 1991.
  • Mendelson, E., Introduction to Mathematical logic . 4th ed. Springer, 1997.
Lecture notes