Sökresultat: 3
Logic II is a second level logic course, giving an introduction to major topics of modern mathematical logic. It consists of three main parts:
- axiomatic foundations: Zermelo–Fraenkel set theory, and the development of mathematics therein, including ordinals, cardinals, transfinite recursion, the axiom of choice and its applications, and first independence results
- model theory: structures and isomorphisms, elementary equivalence and embeddings, the Löwenheim–Skolem theorems, categoricity, back-and-forth arguments, and applications/examples including non-standard analysis
- computability and incompleteness: models of computability; (un)decidability and (un)computability; coding of logic, and Gödel’s incompleteness theorems.
The course literature is R. Cori, D. Lascar, 2001, Mathematical logic, a course with exercises, Part II: Recursion Theory, Gödel’s Theorems, Set Theory, Model Theory (Oxford University Press); SU library details.
The main prerequisite course is MM5024 (Mathematics III — Logik) or equivalent; precise prerequisites, full kursplan etc. are here.
Please note that self-enrollment on the course page is not the same as course registration in Ladok.
- Teacher: Peter LeFanu Lumsdaine
Logic is the study of reasoning.
In the middle of the 19th century Boole and others started to study logic with mathematical methods, e.g. Boolean algebra, which gave rise to formal logic. The treatment of logic as a mathematical subject is indispensible in both mathematics and computer science, and opens the possibility for analysing and automating many intellectual tasks, including even mathematical reasoning itself.
This course is intended as a first course in logic. It treats the two most important logics, propositional logic and predicate logic, in depth, and shows how they are used in modelling reasoning, especially mathematical reasoning. In particular, we define and study the formal language of predicate logic, its semantics (models), and natural deduction for it. We will prove soundness and completeness of natural deduction with respect to the semantics, and give some applications of these theorems.
Please note that self-enrollment on the course page is not the same as course registration in Ladok.
- Teacher: Sofia Tirabassi
- Teacher: Errol Yuksel
Logic is the study of reasoning.
In the middle of the 19th century Boole and others started to study logic with mathematical methods, e.g. Boolean algebra, which gave rise to formal logic. The treatment of logic as a mathematical subject is indispensible in both mathematics and computer science, and opens the possibility for analysing and automating many intellectual tasks, including even mathematical reasoning itself.
This course is intended as a first course in logic. It treats the two most important logics, propositional logic and predicate logic, in depth, and shows how they are used in modelling reasoning, especially mathematical reasoning. In particular, we define and study the formal language of predicate logic, its semantics (models), and natural deduction for it. We will prove soundness and completeness of natural deduction with respect to the semantics, and give some applications of these theorems.
Please note that self-enrollment on the course page is not the same as course registration in Ladok.
- Teacher: Boris Shapiro
- Teacher: Errol Yuksel