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.

Ilmoittaudu
11.2.2019 klo 09:00 - 30.4.2019 klo 23:59

Viestit

Käyttäjän Jouko Väänänen kuva

Jouko Väänänen

Julkaistu, 21.5.2019 klo 11:05

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

Käyttäjän Jouko Väänänen kuva

Jouko Väänänen

Julkaistu, 14.5.2019 klo 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.

Käyttäjän Jouko Väänänen kuva

Jouko Väänänen

Julkaistu, 14.5.2019 klo 8:43

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

Käyttäjän Jouko Väänänen kuva

Jouko Väänänen

Julkaistu, 8.5.2019 klo 21:46

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

Käyttäjän Jouko Väänänen kuva

Jouko Väänänen

Julkaistu, 10.4.2019 klo 8:52

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

Käyttäjän Jouko Väänänen kuva

Jouko Väänänen

Julkaistu, 10.4.2019 klo 8:51

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

Aikataulu

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.

PäivämääräAikaOpetuspaikka
Ma 11.3.2019
10:15 - 12:00
Ti 12.3.2019
10:15 - 12:00
Ti 12.3.2019
14:15 - 16:00
Ma 18.3.2019
10:15 - 12:00
Ti 19.3.2019
10:15 - 12:00
Ti 19.3.2019
14:15 - 16:00
Ma 25.3.2019
10:15 - 12:00
Ti 26.3.2019
10:15 - 12:00
Ti 26.3.2019
14:15 - 16:00
Ma 1.4.2019
10:15 - 12:00
Ti 2.4.2019
10:15 - 12:00
Ti 2.4.2019
14:15 - 16:00
Ma 8.4.2019
10:15 - 12:00
Ti 9.4.2019
10:15 - 12:00
Ti 9.4.2019
14:15 - 16:00
Ma 15.4.2019
10:15 - 12:00
Ti 16.4.2019
10:15 - 12:00
Ti 16.4.2019
14:15 - 16:00
Ma 29.4.2019
10:15 - 12:00
Ti 30.4.2019
10:15 - 12:00
Ti 30.4.2019
14:15 - 16:00
Ti 14.5.2019
10:15 - 14:00

Materiaalit

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

Kuvaus

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