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Abstract: Recently, Coquand and Palmgren considered systems of intuitionistic arithmetic in all finite types together with various forms of the axiom of choice and a numerical omniscience schema (NOS) which implies classical logic for arithmetical formulas. Feferman subsequently observed that the proof theoretic strength of such systems can be determined by functional interpretation based on a non-constructive -operator and his well-known results on the strength of this operator from the 70's. In this... (Update)
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.... A 3 corresponds to the lesser limited principle of omniscience, LLPO : #x # R(x # 0 # x # 0) as shown in [Ish90] see also [Koha], Man88] HN] and [CP00] The semi classical systems A 2 and A 3 have been analysed in e.g. Koha] and [Koh98b] Future work in this area...
.... A(x) A(x) 8x 2 N:A(x) 9x 2 N: A(x) which is clearly related to the discussion above, has been considered by several authors, [7, 14]. Iterated applications of this scheme implies 6 0 n LEM in HA and the system turns to PA. Namely, NOS maintains that realizers are closed...
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BibTeX entry: (Update)
U. Kohlenbach. Intuitionistic choice and restricted classical logic. To appear in: Math. Logic Quaterly, 9 pages. http://citeseer.ist.psu.edu/kohlenbach00intuitionistic.html More
@misc{ kohlenbach-intuitionistic,
author = "U. Kohlenbach",
title = "Intuitionistic choice and restricted classical logic",
text = "U. Kohlenbach. Intuitionistic choice and restricted classical logic. To
appear in: Math. Logic Quaterly, 9 pages.",
url = "citeseer.ist.psu.edu/kohlenbach00intuitionistic.html" }
Citations (may not include all citations):104 Metamathematical investigation of intuitionistic arithmetic .. (context) - Troelstra - 1973
30 Theories of finite type related to mathematical practice (context) - Feferman - 1977
25 Varieties of Constructive Mathematics (context) - Bridges, Richman - 1987
20 Dialectica (context) - Avigad, Feferman - 1998
16 Hereditarily majorizable functionals of finite type (context) - Howard
15 Note on the fan theorem (context) - Troelstra - 1974
12 Studies in Logic and the Foundations of Mathematics Vol (context) - Buss - 1998
12 Extensional Godel functional interpretation (context) - Luckhardt - 1973
9 ective bounds from ine#ective proofs in analysis: an applica.. (context) - Kohlenbach - 1992
9 Intuitionistic choice and classical logic - Coquand, Palmgren - 2000
7 Relative constructivity - Kohlenbach - 1998
1 Strict Constructivism and the Philosophy of Mathematics (context) - Ye - 1999
1 the proof theoretical strength of some systems with the nume.. (context) - Feferman - 2000
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The Use of a Logical Principle of Uniform Boundedness in Analysis - Kohlenbach (1996) (Correct)
A note on Goodman's theorem - Kohlenbach (1997) (Correct)
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