# Math 125A - Mathematical Logic

Fall 2008

### Overview

Lectures: TuTh 1230-2pm, Room 3 Evans
Instructor: Jan Reimann
Office: 705 Evans Hall
Office hours: Tu 4-5, We 10-12 and by appointment
Email:
Personal Website: http://math.berkeley.edu/~reimann/

Course webpage: This site is mainly for documetary purposes. The course material (homework, sample exams, etc.) will be posted on bSpace. The course site will also has a chat room. I encourage you to make use of it. Go to http://bspace.berkeley.edu and log on with your Calnet ID. Then select the tab "MATH 125A Fa08".

### Content

Propositional logic; predicate logic, syntax of first order logic, semantics, structures, satisfaction relation; logic of first order structures, substructures and elementary substructures, definable sets, example: dense linear orders; the Loewenheim-Skolem-Theorem; Goedel Completeness Theorem, Henkin constructions; the Compactness Theorem, types; quantifier elimination, examples: dense linear orders, real closed fields; incompleteness, Goedel's Theorems

### Text

We will use lecture notes by Slaman and Woodin. These are provided on the bSpace site for the course.

Supplementary reading. There are many introductory logic texts. Two frequently used ones are Enderton's A Mathematical Introduction to Logic, and Mathematical Logic by Ebbinghaus, Flum, and Thomas. Both are good texts, and I certainly recommend looking at them if you want a different angle on some material of the course. If you want to delve deeper into the many aspects of mathematical logic, take a look at Shoenfield's Mathematical Logic. This is quite an old book, and aimed rather at the graduate level, but there are still few texts that can keep up with this classic.

### Exams

There will be one midterm in class: Thursday, Oct 16. If you miss the midterm with a valid excuse, your score in the final exam will count for 75% of the grade. There will be no makeup exams.

The final exam is held on Friday, December 19, 1230-330pm, room TBA

All exams will be closed book exams. No cheat sheets! Bring blue books.

### Homework

Homework will be assigned on Thursday and will be due on the following Thursday in class. Homework will be graded and the two lowest scores will be dropped. Late homework will not be accepted. There will be no exception to this rule. Of course it may happen that you cannot turn in homework because you were ill or for some other valid reason. This is why the two lowest scores will be dropped.

A note on academic honesty: Collaboration among students to solve homework assignments is welcome. This is a good way to learn mathematics. So is the consultation of other sources such as other textbooks. However, every student has to hand in an own set of solutions, and if you use other people's work or ideas you should indicate the source in your solutions.
(In any case, complete and correct homework receives full credit.)