Kaisa_2012_3_photo by Veikko Somerpuro

Strong Logics

The main topics are generalized quantifiers, infinitary logics and second order logic.
Methods are model and set theoretic.

The course will cover the basics of strong logics, such as generalized quantifiers, infinitary logic and second order logic, especially from the point of view of interaction between model theory and set theory. An example of a generalized quantifier is the quantifier "There are uncountably many". In infinitary logic we allow infinite disjunctions and conjunctions. In second order logic quantification over subsets of the domain is allowed. Strong logics can express mathematical properties that go beyond first order logic, such as connectivity of a graph, torsion-freeness of an abelian group, finiteness of a predicate, etc. In general, set theoretical methods are needed in developing model theory of strong logics. On the other hand, strong logics give rise to interesting set theoretical questions, such as large cardinal properties and reflection principles.

Enrol
11.2.2019 at 09:00 - 30.4.2019 at 23:59

Messages

Jouko Väänänen's picture

Jouko Väänänen

Published, 21.5.2019 at 11:05

Final exam has been moved to 7.8.2019 (yleistentti). You have to register to the the exam in May.

Jouko Väänänen's picture

Jouko Väänänen

Published, 14.5.2019 at 8:54

Registration to the final exam (ilmoittautuminen loppukokeeseen)

https://weboodi.helsinki.fi/hy/opettaptied.jsp?OpetTap=129538542&html=1

Deadline is 31.5.2019.

Jouko Väänänen's picture

Jouko Väänänen

Published, 14.5.2019 at 8:43

Final exam is 12.6.2019, at 10.00 - 13.00 in CK112.

Jouko Väänänen's picture

Jouko Väänänen

Published, 8.5.2019 at 21:46

The final exam is June 12. Time and place TBA.

Jouko Väänänen's picture

Jouko Väänänen

Published, 10.4.2019 at 8:52

April 30th lecture and problem session have been moved to May 14, 10-12 and 12-14, lecture room C322.

Jouko Väänänen's picture

Jouko Väänänen

Published, 10.4.2019 at 8:51

April 30th lecture and problem session have been moved to May 14, lecture room C322.

Timetable

Monday and Tuesday 10-12 are the lecture times.
Tuesday 14-16 is the Problem Session time.
April 30th lecture and problem session have been moved to May 14, 10-12 and 12-14, lecture room C322.

DateTimeLocation
Mon 11.3.2019
10:15 - 12:00
Tue 12.3.2019
10:15 - 12:00
Tue 12.3.2019
14:15 - 16:00
Mon 18.3.2019
10:15 - 12:00
Tue 19.3.2019
10:15 - 12:00
Tue 19.3.2019
14:15 - 16:00
Mon 25.3.2019
10:15 - 12:00
Tue 26.3.2019
10:15 - 12:00
Tue 26.3.2019
14:15 - 16:00
Mon 1.4.2019
10:15 - 12:00
Tue 2.4.2019
10:15 - 12:00
Tue 2.4.2019
14:15 - 16:00
Mon 8.4.2019
10:15 - 12:00
Tue 9.4.2019
10:15 - 12:00
Tue 9.4.2019
14:15 - 16:00
Mon 15.4.2019
10:15 - 12:00
Tue 16.4.2019
10:15 - 12:00
Tue 16.4.2019
14:15 - 16:00
Mon 29.4.2019
10:15 - 12:00
Tue 30.4.2019
10:15 - 12:00
Tue 30.4.2019
14:15 - 16:00
Tue 14.5.2019
10:15 - 14:00

Material

There will be a set of slides that will be available online. In addition the blackboard is used for detailed arguments.

Description

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Set theory, model theory

Master studies

Basic knowledge of the set theory of strong logics

Recommended time/stage of studies for completion: 1. or 2. year

Term/teaching period when the course will be offered: varying

Strong logics, completeness theorems

Lecture notes

Lectures

Exam and excercises, Course will be graded with grades 1-5

Exam, other methods will be described later