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Abstract: this paper addresses `1),' to which S. Feferman has contributed so profoundly. We study mathematical strong, but nevertheless PRA-redu- (Update)
Context of citations to this paper: More
...is the weakest one that is rich enough to express and develop the bulk of core mathematics ( 16] p. viii) However, as we have argued in [14], already the treatment of continuous functions f : X # Y between Polish spaces X,Y not only requires a quite complicated encoding....
.... PRA (and even much weaker systems) have been developed by the author in a series of papers (see e.g. 8] 9] and for a general survey [15]) These facts are of interest for mainly two reasons 1) If a 0 2 sentence A is provable in T and the conservation of T over PRA has...
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5: Subsystems of second-order arithmetic (context) - Simpson
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BibTeX entry: (Update)
Kohlenbach, U., Foundational and mathematical uses of higher types. To appear in forthcoming Festschrift in honor of Professor Solomon Feferman. http://citeseer.ist.psu.edu/article/kohlenbach00foundational.html More
@misc{ kohlenbach-foundational,
author = "U. Kohlenbach",
title = "Foundational and mathematical uses of higher types",
text = "Kohlenbach, U., Foundational and mathematical uses of higher types. To
appear in forthcoming Festschrift in honor of Professor Solomon Feferman.",
url = "citeseer.ist.psu.edu/article/kohlenbach00foundational.html" }
Citations (may not include all citations):104 Metamathematical investigation of intuitionistic arithmetic .. (context) - Troelstra - 1973
69 A language and axioms for explicit mathematics (context) - Feferman - 1975
62 Subsystems of Second Order Arithmetic (context) - Simpson - 1999
44 Uber eine bisher noch nicht benutzte Erweiterung des finiten.. (context) - Godel - 1958
30 Theories of finite type related to mathematical practice (context) - Feferman - 1977
20 Dialectica (context) - Avigad, Feferman - 1998
20 Mathematically strong subsystems of analysis with low rate o.. - Kohlenbach - 1996
18 Fragments of arithmetic (context) - Sieg - 1985
17 Electronic Notes in Theoretical Computer Science (context) - Kohlenbach - 1998
15 Note on the fan theorem (context) - Troelstra - 1974
14 Pointwise hereditary majorization and some applications - Kohlenbach - 1992
14 Arithmetizing proofs in analysis - Kohlenbach - 1998
13 Real growth in standard parts of analysis (context) - Kohlenbach - 1995
12 Studies in Logic and the Foundations of Mathematics Vol (context) - Buss - 1998
12 Partial realizations of Hilbert's program (context) - Simpson - 1988
11 Springer Lecture Notes in Mathematics (context) - Normann - 1980
10 Remarks on Herbrand normal forms and Herbrand realizations (context) - Kohlenbach - 1992
10 Lecture Notes in Mathematics (context) - Felgner - 1971
10 ective moduli from ine#ective uniqueness proofs (context) - Kohlenbach - 1993
9 Journal of Philosophy (context) - Tait - 1981
9 ective bounds from ine#ective proofs in analysis: an applica.. (context) - Kohlenbach - 1992
9 Two applications of logic to mathematics (context) - Takeuti, extension - 1978
8 The Boolean Prime Ideal theorem does not imply the axiom of .. (context) - Halpern, --Levy - 1971
8 the no-counterexample interpretation - Kohlenbach - 1999
7 Springer Ergebnisse der Mathematik und ihrer Grenzgebiete (context) - Beeson - 1985
6 The use of a logical principle of uniform boundedness in ana.. - Kohlenbach - 1999
5 Things that can and things that can't be done in PRA - Kohlenbach - 2000
5 the arithmetical content of restricted forms of comprehensio.. - Kohlenbach - 1998
5 Infinity in mathematics: Is Cantor necessary (context) - Feferman - 1987
5 Higher order reverse mathematics - Kohlenbach
4 Why a little bit goes a long way: Logical foundations of sci.. (context) - Feferman - 1992
4 Weyl vindicated: Das Kontinuum seventy years later (context) - Feferman - 1988
4 the uniform weak Konig's lemma - Kohlenbach
3 Working foundations (context) - Feferman - 1985
2 The axiom of choice and two definitions of continuity (context) - Jagermann - 1965
1 FOUNDATIONAL AND MATHEMATICAL USES OF HIGHER TYPES (context) - Grilliot, On et al. - 1971
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.daimi.aau.dk/~kohlenb/): More
A note on Goodman's theorem - Kohlenbach (1997) (Correct)
The Use of a Logical Principle of Uniform Boundedness in Analysis - Kohlenbach (1996) (Correct)
On the computational content of the Krasnoselski and Ishikawa.. - Kohlenbach (2000) (Correct)
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