# Introduction to Mathematical Logic

### Course content

First order logic, languages, models and examples. Formal deduction, deduction metatheorems, soundness, completeness and compactness, and applications of compactness. Basic axiomatic set theory, ordinals, cardinals, and the von Neumann hierarchy of sets, and its relation to the iterative concept of set.

Education

MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject

Learning outcome

Knowledge:
The participants are expected to acquire the knowledge listed above in the course description.

Skills:
The participants are expected to be able to define the satisfacation relation, account for the axioms of the deductive system, and use the compactness theorem to construct models and counterexamples. The student must be able to prove the key theorems of the course, such as the deduction theorem, the soundness theorem, completeness theorem, and the compactness theorem. The student must be able to apply the theorem schema of recursion on the ordinals, and prove theorems by induction on the ordinals.

Competences:
The participants are expected to master the most fundamental concepts and constructions in mathematical logic and axiomatic set theory, which are used in further studies in logic and set theory.

4 hours lecture and 3 hours tutorials per week for 7 weeks.

Example of course litterature:

H. Enderton: A Mathematical Introduction to Logic

Academic qualifications equivalent to a BSc degree in mathematics is recommended. At a minimum, the student should have completed courses equivalent to the first 2 full years of a mathematics BSc program offered by the Copenhagen Department of Mathematical Sciences, and must have taken DisMat, LinAlg, and Alg1.

Continuous feedback during the course
ECTS
7,5 ECTS
Type of assessment
Written assignment, 27 hours
Type of assessment details
Written take-home assignment 27 hours (9am Monday to 12pm Tuesday in week 8 of the block. If Monday is a holiday, the exam will start on a Tuesday instead, and end on a Wednesday).
Aid
All aids allowed
Marking scale
Censorship form
No external censorship
One internal examiner
##### Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

• Category
• Hours
• Lectures
• 28
• Preparation
• 146
• Theory exercises
• 21
• Exam
• 11
• English
• 206

### Kursusinformation

Language
English
Course number
NMAA13036U
ECTS
7,5 ECTS
Programme level
Full Degree Master
Duration

1 block

Placement
Block 3
Schedulegroup
B
Capacity
No limit
The number of seats may be reduced in the late registration period
Studyboard
Study Board of Mathematics and Computer Science
##### Contracting department
• Department of Mathematical Sciences
##### Contracting faculty
• Faculty of Science
##### Course Coordinator
• Asger Dag Törnquist   (6-6b7d716f7c7e4a776b7e7238757f386e75)
Phone +45 35 32 07 57, office 04.2.17
Saved on the 28-02-2022

### Are you BA- or KA-student?

Are you bachelor- or kandidat-student, then find the course in the course catalog for students:

Courseinformation of students