## Realizability: An Introduction to its Categorical SideAimed at starting researchers in the field, Realizability gives a rigorous, yet reasonable introduction to the basic concepts of a field which has passed several successive phases of abstraction. Material from previously unpublished sources such as Ph.D. theses, unpublished papers, etc. has been molded into one comprehensive presentation of the subject area.- The first book to date on this subject area - Provides an clear introduction to Realizability with a comprehensive bibliography - Easy to read and mathematically rigorous - Written by an expert in the field |

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### Contents

1 | |

Chapter 2 Realizability triposes and toposes | 49 |

Chapter 3 The Effective Topos | 115 |

Chapter 4 Variations | 255 |

291 | |

305 | |

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### Common terms and phrases

2-category applicative morphism arithmetic arrow f Ass(A Ass(B axiom Beck-Chevalley condition closed subobject codes codomain colimits commutes complete construction coproduct Corollary countable defined definition denote discrete map domain effective topos element epimorphism equivalence relation example Fam(C fibration finite limits formula full subcategory function f functional relation geometric morphism given hence Heyting algebra holds induced interpretation intuitionistic isomorphic Kleene left adjoint Lemma logic map f morphism f natural numbers object nonempty order-pca pair partial function partial recursive function partitioned assembly predicate preorder preserves finite primitive recursive principle projective objects Proof Proposition prove pullback pullback diagram quotient realizability tripos recursion theory represented right adjoint RT(A S-functor satisfies sequence strict relation subset subtopos Suppose surjection theorem topos theory toposes total recursive function transformation tripos uniform unique variables ZF-algebra