## Godel's ProofIn 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times." |

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### Contents

1 | |

7 | |

III Absolute Proofs of Consistency | 25 |

IV The Systematic Codification of Formal Logic | 37 |

V An Example of a Successful Absolute Proof of Consistency | 45 |

VI The Idea of Mapping and Its Use in Mathematics | 57 |

VII Gödels Proofs | 68 |

VIII Concluding Reflections | 109 |

Notes | 114 |

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