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Introduction to Mathematical Logic
Provider: Faculty of Science

Activity no.: 5601-19-07-31 
Enrollment deadline: 18/04/2019
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time23.04.2019, at: 09:00 - 23.06.2019, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserAsger Dag Törnquist    E-mail address: asgert@math.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockBlock 4
Scheme groupC
Exam requirementsTo 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.
Exam formWritten assignment
Exam formWritten assignment, 72 hours
Exam detailsCHANGED FOR THE STUDY YEAR 2018/19 Written take-home assignment 3 days (9am Monday to 9am Thursday in week 8 of the block.
Course workload
Course workload categoryHours
Lectures28.00
Theory exercises21.00
Preparation117.00
Exam40.00
Sum206.00
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 and cardinals. Towards the end of the course, other topics such as recursion theory, computable functions on the natural numbers, Turing machines, recursively enumerable sets, and arithmetization of first order syntax may be discussed.

Learning outcome
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; arithmetization of first order syntax; the axioms of Zermelo-Fraenkel set theory; ordinals and cardinals.

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. 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.

Competences: Use of first order languages and structures in mathematics, the formalization of proofs, proof methods based on the compactness. Use ordinal analysis and transfinite recursion.

Literature
H. Enderton: A Mathematical Introduction to Logic

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

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