Bu sayfada, Bruno Poizat tarafından verilecek olan model teori giriş dersi ve seminer dizisi ile ilgili bilgiler bulunmaktadır.

On this page: information about a model theory course and seminar to be given by Bruno Poizat.

Model teoriye giriş dersi
Introductory model theory course

(Bu ders, MSGSÜ Matematik Bölümünün MAT 414 dersinin parçasıdır.)

Dersin Kısa Tanıtımı (A short introduction to the course):

This course will offer an exposition of the present developments of the branch of Mathematical Logic which is called Model Theory, assuming from the students only a basic knowledge of the kind of properties of a structure that can be expressed in first order logic. It will combine a recently discovered approach to the subject with application to algebraic stuctures of a general interest in mathematics.

Yer (Place):

Mimar Sinan Üniversitesi, Matematik Bölümü, Silahşör Cad. 71, Bomonti, Şişli

Derse Hazırlık: 13 Şubat–5 Mart 2012 (Preparatory course: February 13–March 5, 2012)

Öğretim Üyesi (Instructor):

David Pierce (MSGSÜ)

Dil (Language):

Türkçe

Ders saatleri (Course hours):

Pazartesi ve Çarşamba (Monday and Wednesday) 14.00–15.50

Konular (Topics):

1. manipulation of boolean formulae: negation only in front of atomic formulae, disjunction of conjunctions; prenex form of quantified formulae
2. compactness (proof not necessary), and some easy applications
3. elimination in the complexes and in the reals (idem)
4. theories and models, elementary equivalence and elementary extension
5. infinite back and forth

Ders: 7 Mart–11 Nisan 2012 (The course itself: March 7–April 11, 2012)

Öğretim Üyesi (Instructor):

Bruno Poizat (Lyon Üniversitesi)

Dil (Language):

Türkçe

Ders Saatleri (Course hours):

Pazartesi ve Çarşamba 13.00–15.50 (Haftada 4 saat ders, 2 saat tartışma)

Konular (Topics):

1. Inductive limit of groups, existentially closed (ec) groups; types and independance in ec groups: free products and free group
2. Inductive limits of fields, algebraically closed fields; types and independence in algebraically closed fields.
3. Inductive limits of formally real fields, real closed fields
4. Inductive limits of structures in general, inductive sentences, existentially closed models of an inductive theory
5. Compactness for inductive theory (with a full and short proof)
6. Companion theories; characterization of ec models; model-complete theories
7. Morleyisation: how to interpret any theory into an inductive one; compactness of first order logic with negation.
8. Amalgamation of homomomorphisms
9. Spaces of types; addition of clopen sets, or of closed sets, to the language
10. Quotient of a structure by a definable or infinitely definable equivalence relation
11. Dimension theory: Cantor and Morley ranks, with application to the case of groups of finite Morley rank

Model teori seminer dizisi (Model theory seminar)

(These talks are part of the Istanbul Model Theory Seminar.)

Tarihler (Dates):

8 Mart 2012–

Dil (Language):

English

Saatler (Hours):

Perşembe günleri (Thursdays) 15.00–16.50

Yer (Place):

MSGSÜ Matematik Bölümü veya Bilgi Üniversitesi Matematik Bölümü (Dolapdere Kampüsü)

Konu (Topics):

The seminar will be centered on questions concerning the theory of models for groups, mainly for the groups bearing a notion of dimension (the so-called groups of finite Morley rank), or for groups sharing with them some properties allowing a control of their definable sets. Indeed, many mathematicians presently residing in Istanbul are active in the subject.

A considerable number of works have been produced with an aim at classification of the simple groups of finite Morley rank, finding somehow their inspiration in the classification of simple finite groups; the expectation is that all these groups will be algebraic groups over an algebraically closed field.

Since this approach has not be fully conclusive for the moment, the seminar will focus its attention more on logic than algebra, and will try to evaluate the distance between algebraic groups and groups of finite Morley rank, for instance by considering some model-theoretic properties of algebraic groups that are far from being obvious in the case of groups of finite Moley rank.

Slides