|
Instructor: Prof. Dr. Benedikt
Löwe
Vakcode: 5314SEML3Y
ECTS: 3
Time & Place:
Wednesday 15-19, SP107 F1.16
Course language: English
Intended audience:
M.Sc. students of Logic specializing in mathematical logic.
Topic of this course:
Extensions of first-order logic.
Evaluation: The course is graded on a pass/fail
basis. In order to pass, a student will have to give a presentation in
class.
Schedule.
| 6 February 2013 |
15-17
| Benedikt Löwe.
| Introduction to the theme of the seminar and the various topics.
Distribution of tasks to the students.
|
|---|
| 17-19
| Alexander Block. | Lindström's Theorem.
|
|---|
| 20 February 2013 |
15-17
|
Yuning Feng,
Iva Gornishka,
Nikhil Maddirala,
Deniz Sarikaya.
| Second-order logic vs. many-sorted logic. Syntax
and Semantics of many-sorted logic. Syntax and Semantics of second-order
logic. Expressivity results and impossibility results (status of
compactness, completeness and Löwenheim-Skolem). Representation of
second-order logic in many-sorted logic.
Literature.
- Jean H. Gallier, Many-Sorted First-Order Logic, Chapter 10 of
"Introduction to the Theory of Computation", 2004: PostScript file.
- Jouko Väänänen, Second-Order Logic and Foundations
of Mathematics, Bulletin of Symbolic Logic 7:4 (2001),
pp.504-520.
- Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas,
Mathematical Logic, Springer-Verlag 1994 [Undergraduate Texts in
Mathematics]
|
|---|
| 17-19
|
|---|
| 27 February 2013 |
15-17
|
|---|
| 17-19
|
|---|
| 6 March 2013 |
15-17
|
Simon Docherty,
Evante Garza-Licudine.
| Infinitary logic. Syntax and Semantics of
Lω1ω. Expressive power of infinitary logics in comparison to first-order logic. Status of completeness, compactness and Löwenheim-Skolem.
Literature.
-
Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas,
Mathematical Logic, Springer-Verlag 1994 [Undergraduate Texts in
Mathematics]
- Dave Marker, A Primer on Infinitary Logic. PDF file.
|
|---|
| 17-19
|
Adam Crager,
Justin Kruger,
Andrea Nespola.
| Generalized quantifiers. Definitions of generalized
quantifiers. Examples. Definability.
Literature.
- Per Lindstöm, First order predicate logic with generalized
quantifiers, Theoria 32:3 (1966), pp. 186-195. PDF
file
- Lauri Hella, Definability hierarchies of generalized quantifiers, Annals of Pure and Applied Logic 43 (1989), pp. 235-271. publisher's webpage
- Lauri Hella, Kerkko Luosto, Jouko Väänänen, The hierarchy theorem for generalized quantifiers, Journal of Symbolic Logic 61 (1996), pp. 802-817. PDF file.
|
|---|
| 13 March 2013 |
15-17
|
|---|
| 17-19
|
|---|
| 20 March 2013 |
15-17
|
Hans Grathwohl,
Zhiguang Zhao.
|
ω-logic. Syntax and Semantics of ω-logic. Proof of
the completeness of arithmetic in ω-logic. Connections between
ω-logic, ω-consistency and Gödel's second
incompleteness theorem.
Literature. C.C. Chang, H. Jerome Keisler, Model Theory,
North-Holland 1990 [Studies in Logic and the Foundations of Mathematics
73]
|
|---|
| 17-19
|
|---|
| 3 April 2013 |
17-19
|
Alexander Block,
Julia Ilin,
Tanmay Inamdar,
Hugo Nobrega,
Apostolos Tzimoulis.
| Subsystems of second-order arithmetic.
Lévy hierarchy of formulas. The definitions of the five main systems
of reverse mathematics. Separation of the systems by construction of models.
β-models. ω-models.
Literature. Steve Simpson, Subsystems of Second Order Arithmetic,
Second Edition, Cambridge University Press 2010 [Perspectives in Logic]
|
|---|
| 10 April 2013 |
17-19
|
|---|
| 17 April 2013 |
17-19
|
|---|
| 24 April 2013 |
17-19
|
|---|
|
