Foundation of logic and set theory

Language (EN))(FA)

Instructor: S. M. A. Khatami
Office: 316
phone: 32391444
e-mail: khatami@birjandut.ac.ir
 

Description

A first graduate course in mathematical logic. We will introduce the fundamental themes of mathematical logic (truth, provability, and computability), discuss their interconnections and examine the power and limits of formal methods. The main results will be Godel's Completeness and Incompleteness Theorems and Tarski's decidability results for the real and complex fields. Specific topics covered will include.

• Propositional logic
• Formal proofs and soundness Theorem
• The Completeness Theorem
• The Compactness Theorem
• Boolean algebras
• First-order logic
• Mathematical structures
• Formal proofs
• Completeness and Compactness Theorem and elementary model theory
• Introduction to set theory theory
• Cardianal arithmetic
• Ordinal arithmetic

Texts

• M. Ardeshir, Mathematical logic (in Persian)
• H.-D. Ebbinghaus, J. Flum and W. Thomas, Mathematical Logic Second Edition, Springer-Verlag, 1994.
• N. Cutland, Computability: An introduction to recursive function theory, Cambridge University Press, 1986.

  Prerequisites

  Graduate standing. No previous background in logic is assumed. As many examples will come from Algebra, Math 516 is a useful.

  Grading

• I will give out about 8 problem sets. You may work together on homework problems (and I encourage you to do so), but when you turn in the problem you should acknowledge that you have worked together. There will probably be a one hour final exam testing basic concepts, definitions, and statements of theorems.
   

  Homework Assignments

  • Problem Set 1
  • Problem Set 2
  • Problem Set 3
  • Problem Set 4
  • Problem Set 5
  • Problem Set 6
  • Problem Set 7
  
  S. M. A. Khatami's Home Page