## The Calculi of Lambda-conversionThe description for this book, The Calculi of Lambda Conversion. (AM-6), Volume 6, will be forthcoming. |

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This book should be off copyright and offered to the public as a out of copyright work.

Church has been dead for 34 years, and Princton is the only institution making money off of this and likely not very much money.

I call out that this is BS that this book is completely open and free to use in classrooms, personal studies, etc.

### Contents

INTRODUCTORY | 1 |

LAMBDACONVERSION | 8 |

Continued | 22 |

LAMBDADEFINABILITY | 28 |

COMBINATIONS GODEL NUMBERS | 43 |

THE CALCULI OP AKCONVERSION AND A6 | 58 |

Index of the principal formulas introduced by definition | 72 |

Corrections and additions | 82 |

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### Common terms and phrases

6-normal A-6-conversion A-defines the property A-definition abbreviation Alonzo Church Andrzej Mostowski applications of Rule bination calculus of A-conversion characteristic function cnvt combination belonging combinatory combinatory logic contain no free conv conv-I-II defined by primitive definition denotes finite follows formed formula formula representing found which represents free variables func function F function of positive function whose value Gfldel number belonging H conv H represents H. B. Curry Hence hypothesis of induction ibid infinite sequence journal of symbolic Kleene 35 mula notation obtained operations of forming ordered pairs ordered triads Paul Bernays positive integer arguments predecessor function primitive recursive function primitive set principal normal form proof propositional function range of arguments recursion in terms representing a positive represents an enumeration represents the Godel residual Rosser S. C. Kleene sequence of contractions sequence of reductions set of formulas symbolic logic theorems Thoralf Skolem tion tive integer well-formed formula