NMAA13036U Introduction to Mathematical Logic
First order logic, languages, models and examples. Recursion theory, computable functions on the natural numbers, Turing machines, recursively enumerable sets and Turing degrees. Gödel's incompleteness theorems.
Knowledge: By the end of the course, the student is expected to
be able to explain the concepts of: a first order language; of a
model of a first order language; of formal deduction; of a
computable relation and function; and finally, the student should
be able to explain the meaning consistency and incompleteness of a
theory, in particular as it relates to Peano Arithmetic.
Skills: By the end of the course, the student must be able to
define the satisfacation relation, account for the axioms of the
deductive system, define the notion of recursive function, and
prove that a repository of common functions and relations are
recursive, including the coding of basic syntactical notions. The
student must be able to prove the key theorems of the course, such
as the deduction theorem, the soundness theorem, and the first
incompleteness theorem of Gödel.
Competences: Use of first order languages and structures in
mathematics, the formalization of proofs, the coding of
syntactical notions in arithmetic. To explain the incompleteness
phenomenon, and the method of diagonalization.
- Category
- Hours
- Colloquia
- 21
- Exam
- 40
- Excursions
- 2
- Guidance
- 4
- Lectures
- 28
- Preparation
- 70
- Project work
- 20
- Theory exercises
- 21
- Total
- 206
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- Credit
- 7,5 ECTS
- Type of assessment
- Oral examination, 30 minWith preparation time
- Exam registration requirements
- To be eligible to take the final exam the student must have handed in the 2 mandatory homework assignments, and these must both have been approved and have received a passing grade.
- Aid
- Only certain aids allowed
Notes and the text book.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Several internal examiners
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAA13036U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- A (Tues 8-12 + Thurs 8-17)
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Asger Dag Törnquist (6-65776b697678447165786c326f7932686f)