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Abstract: Constructive Mathematics might be regarded as a fragment of classical mathematics in which any proof of an existence theorem is equipped with a computable function giving the solution of the theorem. Limit Computable Mathematics (LCM) considered in this note is a fragment of classical mathematics in which any proof of an existence theorem is equipped with a function computing the solution of the theorem in the limit. (Update)
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BibTeX entry: (Update)
@misc{ nakata-limiting,
author = "Masahiro Nakata and Susumu Hayashi",
title = "A Limiting First Order Realizability Interpretation",
url = "citeseer.ist.psu.edu/498905.html" }
Citations (may not include all citations):412 Language Identification in the Limit (context) - Gold - 1967
143 Foundations of Constructive Mathematics (context) - Beeson - 1985
137 Classical Recursion Theory (context) - Odifreddi
99 Foundations of Constructive Analysis (context) - Bishop - 1967
44 the Interpretation of Intuitionistic Number Theory (context) - Kleene - 1945
39 PX: A Computational Logic (context) - Hayashi, Nakano - 1988
38 Systems that learn-An introduction to learning theory (context) - Jain, Osherson et al. - 1999
32 Trial and Error Predicates and the Solution to a Problem of .. (context) - Putnam - 1965
21 A Semantics of Evidence for Classical Arithmetic (context) - Coquand - 1995
13 the Journal of Symbolic Logic (context) - Gold, Recursion - 1965
12 Springer-Verlag (context) - Invariant - 1993
10 the Computational Content of the Axiom of Choice - Berardi, Bezem et al. - 1998
9 Algebraically Generalized Recursive Function Theory (context) - Strong - 1968
8 On Degrees of Unsolvability (context) - Shoenfield - 1959
5 Machine learning of higher-order programs (context) - Baliga, Case et al. - 1994
4 Towards Animation of Proofs - testing proofs by examples - Hayashi, Sumitomo et al.
3 Limiting Partial Combinatory Algebras Towards Infinitary Lam.. (context) - Akama - 2001
3 Cambridge Mathematical Library (context) - Hilbert, Algebraic - 1993
3 Classical logic as Limit Completion (context) - Berardi - 2001
2 Uber die Theorie der algebraische Formen (context) - Hilbert
2 Towards Limit Computable Mathematics - Hayashi, Nakata - 2001
2 Dezani-Ciancaglini eds (context) - Baratella, Berardi et al.
1 Testing Proofs by Examples (context) - Hayashi, Sumitomo
1 Hilbert's Invariant Theory Papers (context) - Hilbert, by et al. - 1978
Documents on the same site (http://kurt.cla.kobe-u.ac.jp/~hayashi/PALCM/index-eng.html):
Limit Computable Mathematics and Interactive Computation - Susumu Hayashi Kobe (Correct)
Towards Limit Computable Mathematics - Susumu Hayashi And (Correct)
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