## Foundations of constructive mathematics: metamathematical studies |

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### Contents

Part One Practice and Philosophy of Constructive Mathematics | 1 |

Examples of Constructive Mathematics | 3 |

Constructive Reasoning | 5 |

Copyright | |

146 other sections not shown

### Common terms and phrases

algebraic algorithm apply arithmetic atomic formulae axiom of choice Beeson Brouwer Chap Church-Rosser theorem Church's thesis clauses compact complete concept consider constructive mathematics constructive set theory countable defined definition discussion effective operations element equations equivalent example Exercise extension extensional Feferman's theories finite type forcing formal systems free variables given Godel number graph model Hence implies induction initial segment integers interpretation intuitionistic iterative sets Kleene's Lemma Martin-Lofs means metamathematical metric space model of EON natural numbers normal term notation notion pairing partial recursive function PCA+ power set predicate primitive recursive primitive recursive function principle problem proof proof-theoretic proposition provable prove q-realizability real number realizability recursion theorem RED(t reduction rule satisfies schema separable metric space sequence Significus soundness theorem subset Suppose symbols term models transfinite induction Troelstra uniformly continuous