## From Frege to Gödel: a source book in mathematical logic, 1879-1932 |

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### Contents

DEFINITION OF THE SYMBOLS | 10 |

Inference The Aristotelian modes of inference | 17 |

Peano 1889 The principles of arithmetic presented by a new method | 83 |

Dedekind 1890a Letter to Keferstein | 98 |

BuraliForti 1897 and 1897a A question on transfinite numbers | 104 |

Cantor 1899 Letter to Dedekind | 113 |

Russell 1902 Letter to Frege | 124 |

Zermelo 1904 Proof that every set can be wellordered | 139 |

Skolem 1922 Some remarks on axiomatized set theory | 290 |

Skolem 1923 The foundations of elementary arithmetic established | 302 |

Brouwer 1923b 1954 and 1954a On the significance of the principle | 334 |

Schonfinkel 1924 On the building blocks of mathematical logic | 355 |

von Neumann 1925 An axiomatization of set theory | 393 |

Kolmogorov 1925 On the principle of excluded middle | 414 |

Finsler 1926 Formal proofs and undecidability | 438 |

Hilbert 1927 The foundations of mathematics | 464 |

Konig 1905a On the foundations of set theory and the continuum | 145 |

Zermelo 1908 A new proof of the possibility of a wellordering | 183 |

Zermelo 1908a Investigations in the foundations of set theory I | 199 |

Descriptions | 216 |

Wiener 1914 A simplification of the logic of relations | 224 |

Skolem 1920 Logicocombinatorial investigations in the satisfiability | 252 |

Post 1921 Introduction to a general theory of elementary | 264 |

Fraenkel 1922b The notion definite and the independence of | 284 |

Weyl 1927 Comments on Hilberts second lecture on the foundations | 480 |

Ackermann 1928 On Hilberts construction of the real numbers | 493 |

Skolem 1928 On mathematical logic | 508 |

The properties | 525 |

Godel 1930a The completeness of the axioms of the functional | 582 |

Herbrand 193Ib On the consistency of arithmetic | 618 |

657 | |

### Common terms and phrases

according apparent variable applied arbitrary argument arithmetic assertion assume assumption axiom of choice axiom of separation axioms Begriffsschrift belongs Brouwer calculus called Cantor cardinal consider consistency consistency proof constructed contains continuum contradiction corresponding Dedekind defined definition denote denumerably infinite descriptive functions disjoint element equation equivalent example excluded middle exists expression f-sequence false finite number first-order propositions follows footnote formal formula Frege given Godel hence Herbrand Hilbert identity II-object induction inference infinite domain integer intuitionistic judgment Lemma letter logic logical value Lowenheim mapping mathematical mathematical induction means natural numbers negation notion null set objects obtain occur order types ordinal number paper Peano possible predicate prenex form primitive principle of excluded proof propositional function provable prove quantifiers recursive relation replace result Russell satisfied set theory Skolem species subscripts subset theorem tion transfinite truth table truth values well-ordered set well-ordering theorem Zermelo