|| Logic Lecture
|| Péter Mekis
|| BMA-FILD-301.1, BMA-LOTD-102.1, BMI-LOTD-102E.2, BBN-FIL-301.1
|| Friday 10:00-11:30
|| 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.
|| 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.
|| The lectures will cover the following topics:
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.
- introduction: the concept of modern formal logic
and its place in the foundational studies;
- syntax and semantics of
standard first-order languages;
- first-order analytic trees and the decision problem;
- first-order theories: basic concepts and methods;
- Peano arithmetic:
language, definitions, basic theorems,
and the standard model;
- standard first-order calculus:
deductions and metatheorems;
- soundness and completeness of the
standard first-order calculus;
- the compactness theorem and
nonstandard models of Peano arithmetic;
- the downward Löwenheim-Skolem theorem;
- overview of Gödel's incompleteness results;
- higher-order logic;
- definite descriptions and semantic value gaps;
- modal and intensional logic.
- 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