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Abstract: In Russell's Ramified Theory of Types rtt, two hierarchical concepts dominate: orders and types. The use of orders has as a consequence that the logic part of rtt is predicative. The concept of order however, is almost dead since Ramsey eliminated it from rtt. This is why we find Church's simple theory of types (which uses the type concept without the order one) at the bottom of the Barendregt Cube rather than rtt. Despite the disappearence of orders which have a strong correlation with... (Update)
Context of citations to this paper: More
...logics in [LN95, Laa95, Laa96] producing a remarkably legible and formal account of Whitehead and Russell s ideas. Kamareddine and Laan [KL96a] then used this formalization to show that the use of hierarchy of universes in Martin Lof s theory of types and other logical...
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2: A formalization of the Ramified Type Theory - Laan - 1994
BibTeX entry: (Update)
Fairouz Kamareddine and Twan Laan. A correspondence between Nuprl and the ramified theory of types. Technical report, Eindhoven Univerity of Technology, 1996. 12 pages. Available at http://www.win.tue.nl/pub/ techreports/laan/csn96-yy.ps.gz. http://citeseer.ist.psu.edu/kamareddine96correspondence.html More
@misc{ kamareddine96correspondence,
author = "F. Kamareddine and T. Laan",
title = "A correspondence between Nuprl and the ramified theory of types",
text = "Fairouz Kamareddine and Twan Laan. A correspondence between Nuprl and the
ramified theory of types. Technical report, Eindhoven Univerity of Technology,
1996. 12 pages. Available at http://www.win.tue.nl/pub/ techreports/laan/csn96-yy.ps.gz.",
year = "1996",
url = "citeseer.ist.psu.edu/kamareddine96correspondence.html" }
Citations (may not include all citations):474 Term rewriting systems - Klop - 1992
419 A formulation of the simple theory of types (context) - Church - 1940
382 Lambda calculi with types - Barendregt - 1992
266 Information and Computation (context) - Coquand, Huet et al. - 1988
236 Intuitionistic Type Theory (context) - Martin-Lof - 1984
141 Constructive mathematics and computer programming (context) - Martin-Lof - 1982
71 An intuitionistic theory of types: predicative part (context) - Martin-Lof - 1975
56 The formulas-as-types notion of construction (context) - Howard - 1980
50 Cambridge University Press (context) - Whitehead, Russell - 1910
39 Outline of a theory of truth (context) - Kripke - 1975
39 Mathematical logic as based on the theory of types (context) - Russell - 1908
26 The Coq proof assistant version (context) - Dowek - 1991
24 Een nadere bewijstheoretische analyse van GSTT's (context) - Terlouw - 1989
24 Department of Computing Science - Jackson, proof et al. - 1995
23 Studies in Logic and the Foundations of Mathematics (context) - Nederpelt, Geuvers et al. - 1994
22 The Principles of Mathematics - Russell - 1903
13 Grundgesetze der Arithmetik (context) - Frege - 1903
11 Die Grundlehren der Mathematischen Wissenschaften in Einzeld.. (context) - Hilbert, Ackermann et al. - 1928
10 the London Mathematical Society (context) - Ramsey, of et al. - 1925
5 A reflection on Russell's ramified types and Kripke's hierar.. - Kamareddine, Laan - 1996
5 A modern elaboration of the Ramified Theory of Types (context) - Laan
4 Implementing Maths with the Nuprl Proof Development System (context) - Constable - 1986
2 Enhancing the Nuprl Proff Development System and Applying it.. (context) - Jackson - 1995
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