A note on Δ₁ induction and Σ₁ collection
Fundamenta Mathematicae (2005)
- Volume: 186, Issue: 1, page 79-84
- ISSN: 0016-2736
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topNeil Thapen. "A note on Δ₁ induction and Σ₁ collection." Fundamenta Mathematicae 186.1 (2005): 79-84. <http://eudml.org/doc/283324>.
@article{NeilThapen2005,
abstract = {Slaman recently proved that Σₙ collection is provable from Δₙ induction plus exponentiation, partially answering a question of Paris. We give a new version of this proof for the case n = 1, which only requires the following very weak form of exponentiation: "$x^y$ exists for some y sufficiently large that x is smaller than some primitive recursive function of y".},
author = {Neil Thapen},
journal = {Fundamenta Mathematicae},
keywords = {fragments of arithmetic; bounded arithmetic; collection principle},
language = {eng},
number = {1},
pages = {79-84},
title = {A note on Δ₁ induction and Σ₁ collection},
url = {http://eudml.org/doc/283324},
volume = {186},
year = {2005},
}
TY - JOUR
AU - Neil Thapen
TI - A note on Δ₁ induction and Σ₁ collection
JO - Fundamenta Mathematicae
PY - 2005
VL - 186
IS - 1
SP - 79
EP - 84
AB - Slaman recently proved that Σₙ collection is provable from Δₙ induction plus exponentiation, partially answering a question of Paris. We give a new version of this proof for the case n = 1, which only requires the following very weak form of exponentiation: "$x^y$ exists for some y sufficiently large that x is smaller than some primitive recursive function of y".
LA - eng
KW - fragments of arithmetic; bounded arithmetic; collection principle
UR - http://eudml.org/doc/283324
ER -
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