Course Modules

Course Overview

Course Overview
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Course Overview 980077  
  • Attachment
    Syllabus Syllabus
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Introduction to Incompleteness (1/27)

Introduction to Incompleteness (1/27)
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Introduction to Incompleteness (1/27) 979900  
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    [IGT] Chapter 1

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  • Attachment
    Chapter 1: Godel's Incompleteness Theorems by R. Smullyan Chapter 1: Godel's Incompleteness Theorems by R. Smullyan
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  • Context Module Sub Header

    Historical and Philosophical Background

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  • External Url
    Kurt Godel, Stanford Encyclopedia of Philosophy Kurt Godel, Stanford Encyclopedia of Philosophy
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  • External Url
    Hilbert's Program, Stanford Encyclopedia of Philosophy Hilbert's Program, Stanford Encyclopedia of Philosophy
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  • Attachment
    Chapter 1: Godel's Life and Work, in In the Light of Logic by S. Feferman Chapter 1: Godel's Life and Work, in In the Light of Logic by S. Feferman
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Basic Concepts (1/29, 2/3, 2/5)

Basic Concepts (1/29, 2/3, 2/5)
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Basic Concepts (1/29, 2/3, 2/5) 979905  
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    [IGT] Chapter 2-4

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  • Attachment
    Logical Notation Logical Notation
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  • Attachment
    [CL] Chapter 6: Recursive Functions [CL] Chapter 6: Recursive Functions
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    [CL] Chapters 9 & 10: First Order Logic [CL] Chapters 9 & 10: First Order Logic
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  • Assignment
    Problem Set 1 Problem Set 1
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Arithmetic Definability of Recursive Functions (2/10, 2/12)

Arithmetic Definability of Recursive Functions (2/10, 2/12)
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Arithmetic Definability of Recursive Functions (2/10, 2/12) 979907  
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    [IGT] Chapter 15

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  • Attachment
    [CL] Section 16.1: Defining Recursive Functions [CL] Section 16.1: Defining Recursive Functions
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  • Assignment
    Problem Set 2 Problem Set 2
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Formal Arithmetic (2/17, 2/19)

Formal Arithmetic (2/17, 2/19)
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Formal Arithmetic (2/17, 2/19) 979908  
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    [IGT] Chapters 9 - 13

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Capturing (Representing) Numerical Properties (2/24, 2/26)

Capturing (Representing) Numerical Properties (2/24, 2/26)
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Capturing (Representing) Numerical Properties (2/24, 2/26) 979972  
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    [IGT] Chapters 5, 16, 17

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    [CL] Section 16.2: Q is p.r.-adequate [CL] Section 16.2: Q is p.r.-adequate
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Arithmetization of Syntax/Godel Numbering (3/3, 3/5, 3/10)

Arithmetization of Syntax/Godel Numbering (3/3, 3/5, 3/10)
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Arithmetization of Syntax/Godel Numbering (3/3, 3/5, 3/10) 979974  
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    [IGT] Chapters 19 & 20

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    [CL] Chapter 15: Arithematization [CL] Chapter 15: Arithematization
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First Incompleteness Theorem/Diagonal Lemma (3/12)

First Incompleteness Theorem/Diagonal Lemma (3/12)
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First Incompleteness Theorem/Diagonal Lemma (3/12) 979975  
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    [IGT] Chapters 21 - 24

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  • External Url
    Godel's Incompleteness Theorem, Section 2 (SEP) Godel's Incompleteness Theorem, Section 2 (SEP)
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Spring Break --- NO CLASS (3/17, 3/19)

Spring Break --- NO CLASS (3/17, 3/19)
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Spring Break --- NO CLASS (3/17, 3/19) 979976  

Recap, Rosser's Theorem, Tarski's Theorem (3/24, 3/26)

Recap, Rosser's Theorem, Tarski's Theorem (3/24, 3/26)
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Recap, Rosser's Theorem, Tarski's Theorem (3/24, 3/26) 979977  
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    [IGT] Chapters 21 - 24, 25, 27

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  • External Url
    Godel's Incompleteness Theorem, Section 2 (SEP) Godel's Incompleteness Theorem, Section 2 (SEP)
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    Presentation topic Presentation topic
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The Second Incompleteness Theorem (3/31, 4/2)

The Second Incompleteness Theorem (3/31, 4/2)
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The Second Incompleteness Theorem (3/31, 4/2) 979978  
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    [IGT] Chapters 31, 32

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  • External Url
    Godel's Incompleteness Theorem, Section 3 (SEP) Godel's Incompleteness Theorem, Section 3 (SEP)
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Overspill Day (4/7)

Overspill Day (4/7)
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Overspill Day (4/7) 979979  
  • External Url
    Godel's Incompleteness Theorem (SEP) Godel's Incompleteness Theorem (SEP)
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Implications --- Truth vs. Provability (4/9, 4/14)

Implications --- Truth vs. Provability (4/9, 4/14)
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Implications --- Truth vs. Provability (4/9, 4/14) 979981  
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    [IGT] Chapters 23, 37

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  • External Url
    Godel's Incompleteness Theorem, Section 6 (SEP) Godel's Incompleteness Theorem, Section 6 (SEP)
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Lob's Theorem and Provability Logic (4/16, 4/21, 4/23)

Lob's Theorem and Provability Logic (4/16, 4/21, 4/23)
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Lob's Theorem and Provability Logic (4/16, 4/21, 4/23) 979982  
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    [IGT] Chapters 33 & 34

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  • Attachment
    [CL] Chapter 27: Provability Logic [CL] Chapter 27: Provability Logic
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Additional Topics (4/28, 4/30)

Additional Topics (4/28, 4/30)
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Additional Topics (4/28, 4/30) 979984  

Presentations (5/5, 5/7, 5/12)

Presentations (5/5, 5/7, 5/12)
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Presentations (5/5, 5/7, 5/12) 979985  
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    Presentation Notes Presentation Notes
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  • Context Module Sub Header

    Possible Topics

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    Computability and Incompleteness: [IGT] Chapters 40 - 43

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    Speed-Up Theorems: [IGT] Chapter 28

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  • Attachment
    Kirzman and Raz: Surprise Exam & The Second Incompleteness Theorem Kirzman and Raz: Surprise Exam & The Second Incompleteness Theorem
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    Martin Davis: What did Godel Believe? Martin Davis: What did Godel Believe?
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    S. Shapiro: Incompleteness, Mechanism and Optimism S. Shapiro: Incompleteness, Mechanism and Optimism
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  • Attachment
    P. Koellner: Absolute Undecidability P. Koellner: Absolute Undecidability
    Score at least   Must score at least   to complete this module item Scored at least   Module item has been completed by scoring at least   Score at least  % Must score at least  % to complete this module item Scored at least  % Module item has been completed by scoring at least  % View Must view in order to complete this module item Viewed Module item has been viewed and is complete Mark done Must mark this module item done in order to complete Marked done Module item marked as done and is complete Contribute Must contribute to this module item to complete it Contributed Contributed to this module item and is complete Submit Must submit this module item to complete it Submitted Module item submitted and is complete
 
minimum score must view must submit must contribute