Course description:  This course is an introduction to logical meta-theory and elementary meta-mathematics. Topics include consistency, completeness and soundness proofs for propositional and first-order quantified logic, model theory, the axiomatization of number theory (Peano arithmetic), and Gödel's incompleteness theorems and related results.

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CLICK HERE TO VIEW COURSE SYLLABUS - (Includes instructor contact information, textbook information, course requirements and grading policies.)

CLICK HERE TO VIEW COURSE SCHEDULE - (Breakdown of daily readings, homework assignments and due-dates.)

CLICK HERE FOR EXAM 1 - (due Wed., February 23rd) -

CLICK HERE FOR EXAM 2 - (due Fri., April 1st) -

CLICK HERE FOR EXAM 3 - (due Mon., April 25th) -

CLICK HERE FOR EXAM 4 - (due Sun., May 22nd) -

COURSE HANDOUTS AND LECTURE NOTES

• Title Pages and Table of Contents

• UNIT ONE: LOGICAL METATHEORY FOR PROPOSITIONAL LOGIC
  • Pp. 1-3 - Handout one: I. Course Introduction / II. Metalanguage and Object Language
  • Pp. 4-7 - Handout two: III. Set Theory / IV. Mathematical Induction
  • Pp. 8-11 - Handout three: V. Syntax of Propositional Logic / VI. Semantics of Propositional Logic
  • Pp. 11-13 - Handout four: VII. Reducing the Number of Connectives
  • Pp. 14-17 - Handout five: VIII. Axiomatic Systems and Natural Deduction
  • Pp. 18-19 - Handout six: IX. The Deduction Theorem
  • Pp. 20-22 - Handout seven: X. Important Derived Rules for System L / XI. Soundness and Consistency / XII. Completeness
  • Pp. 23-24 - Handout eight: XIII. Independence of the Axioms

• UNIT TWO: LOGICAL META-THEORY FOR FIRST-ORDER PREDICATE LOGIC
  • Pp. 25-27 - Handout one: I. The Syntax of Predicate Logic
  • Pp. 28-32 - Handout two: II. The Semantics of Predicate Logic / III. Countermodels and Semantic Trees
  • Pp. 33-34 - Handout three: IV. An Axiom System / V. The Deduction Theorem in PF
  • Pp. 35-36 - Handout four: VI. Doing Without Existential Instantiation
  • Pp. 36-42 - Handout five: VII. Metatheoretic Results for System PF
  • Pp. 43-46 - Handout six: VIII. Identity Logic
  • Pp. 46-48 - Handout seven: IX. Introducting New Functions Into a Theory Where Appropriate / X. Prenex and Skolem Normal Forms

• UNIT THREE: PEANO ARITHMETIC AND RECURSIVE FUNCTIONS
  • Pp. 49-51 - Handout one: I. The System S
  • Pp. 51-54 - Handout two: II. The Quasi-Fregean System F / III. Some History of Mathematical Logic and Set Theory
  • Pp. 55-58 - Handout three: IV. Numerals / V. Ordering, Complete Induction and Divisibility
  • Pp. 58-60 - Handout four: VI. Expressibility and Representability
  • Pp. 61-65 - Handout five: VII. Primitive Recursive and Recursive Functions
  • Pp. 66-68 - Handout six: VIII. Number Sequence Encoding
  • Pp. 68-70 - Handout seven: IX. Representing Recursive Functions in System S

• UNIT FOUR: GÖDEL'S RESULTS AND THEIR COROLLARIES
  • Pp. 71-73 - Handout one: I. The Basic Idea Behind Gödel's Results
  • Pp. 73-78 - Handout two: II. Arithmetization of Syntax
  • Pp. 78-80 - Handout three: III. Robinson Arithmetic / IV. Diagonalization
  • Pp. 81-84 - Handout four: V. ω-Consistency, True Theories and Completeness / VI. Gödel's First Incompleteness Theorem
  • Pp. 85-88 - Handout five: VII. Church's Thesis / VIII. Löb's Theorem and Gödel's Second Theorem
  • Pp. 88-91 - Handout six: IX. Recursive Undecidability / X. Tarski's Theorem / XI. Church's Theorem

• Indexes of Symbols and Definitions

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