## Fixed point constructions in various theories of mathematical logic |

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### Contents

Fixed point constructions in various theories | 55 |

Fixed point constructions in numeration theory | 71 |

Fixed points in provability logic | 83 |

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### Common terms and phrases

ADNT applications Arithmetic Completeness theorem arithmetic fixed point arithmetical hierarchy arithmetical interpretation axiom schema C(PRA Calculation theorem 5.3.1 Carlson n-model chapt chapter consistent r.e. extension contraposition Corollary Diagonalisation theorem Double Completeness theorem e.i. r.e. sets Ei-formulas equivalence relation extensional formulas fct.s Fixed Point Calculation fixed point constructions fixed point property Fixed Point theorem formal arithmetic formalised Functorial Fixed Point generalisation GFPT GL(Vi hence induction irreflexive Kripke model KSiWSu(Vi m-complete modal logic modal logic system modal operator model theory Mostowski MRFp natural numbers node partial rec Point Calculation theorem prim provability logic prove r.e. relations r.e. sequence recursion theory recursion-theoretic resp Rosser Rosser's theorem S-m-n theorem sect semantic completeness Semantic Completeness theorem Semi-representability semi-represents sequence of consistent Smorynski Solovay Solovay's subformula tail model theorem for numerations theorem for rec total modulo total rec variables Visser's