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Inductionrecursion and initial algebras
 Annals of Pure and Applied Logic
, 2003
"... 1 Introduction Inductionrecursion is a powerful definition method in intuitionistic type theory in the sense of Scott ("Constructive Validity") [31] and MartinL"of [17, 18, 19]. The first occurrence of formal inductionrecursion is MartinL"of's definition of a universe `a la T ..."
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Cited by 28 (11 self)
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1 Introduction Inductionrecursion is a powerful definition method in intuitionistic type theory in the sense of Scott ("Constructive Validity") [31] and MartinL"of [17, 18, 19]. The first occurrence of formal inductionrecursion is MartinL"of's definition of a universe `a la Tarski [19], which consists of a set U
A model for a type theory with Mahlo universe
, 1996
"... We present a type theory T T M, extending MartinLöf Type Theory by adding one Mahlo universe V, a universe being the type theoretic analogue of one recursive Mahlo ordinal. A model, formulated in a KripkePlatek style set theory KP M +, is given and we show that the proof theoretical strength of T ..."
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Cited by 7 (6 self)
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We present a type theory T T M, extending MartinLöf Type Theory by adding one Mahlo universe V, a universe being the type theoretic analogue of one recursive Mahlo ordinal. A model, formulated in a KripkePlatek style set theory KP M +, is given and we show that the proof theoretical strength of T T M is ≤ KP M +  = ψΩ1 (ΩM+ω). By [Se96a], this bound is sharp. 1