Topic
Bar induction
About: Bar induction is a research topic. Over the lifetime, 83 publications have been published within this topic receiving 4822 citations.
Papers published on a yearly basis
Papers
1 Jan 1973
TL;DR: In this paper, Kripke models are used to define inductive definitions, trees and ordinals for intuitionistic formal systems, and normalization theorems for systems of natural deduction.
Abstract: Intuitionistic formal systems.- Models and computability.- Realizability and functional interpretations.- Normalization theorems for systems of natural deduction.- Applications of Kripke models.- Iterated inductive definitions, trees and ordinals.- Erratum.
924 citations
TL;DR: The main results of this paper are interpretations of T0 in intuitionistic arithmetic U0 and of T1 in intuitionist analysis U1 in this paper, where U1 is U0 with quantification over functionals of type (0,0) and the axiom schemata AC00 and of bar induction.
Abstract: T0 will denote Godel's theory T[3] of functionals of finite type (f.t.) with intuitionistic quantification over each f.t. added. T1 will denote T0 together with definition by bar recursion of type o, the axiom schema of bar induction, and the schemaof choice. Precise descriptions of these systems are given below in §4. The main results of this paper are interpretations of T0 in intuitionistic arithmetic U0 and of T1 in intuitionistic analysis is U1. U1 is U0 with quantification over functionals of type (0,0) and the axiom schemata AC00 and of bar induction.
726 citations
Journal Article•
TL;DR: In this article, the conditions générales d'utilisation (http://www.compositio.org/conditions) of the agreement with the Foundation Compositio Mathematica are described.
Abstract: © Foundation Compositio Mathematica, 1968, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
80 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 4 |
| 2020 | 1 |
| 2019 | 6 |
| 2018 | 4 |
| 2017 | 4 |
| 2016 | 7 |