Geodesic
A note on $\Delta _1$ induction and $\Sigma _1$ collection
Neil Thapen1
1 St Hilda's College University of Oxford Oxford OX1 4DY, UK
Fundamenta Mathematicae, Tome 186 (2005) no. 1, pp. 79-84.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Slaman recently proved that $\Sigma _n$ collection is provable from $\Delta _n$ 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 $y$”.
DOI : 10.4064/fm186-1-6
Keywords: slaman recently proved sigma collection provable delta induction plus exponentiation partially answering question paris version proof which only requires following weak form exponentiation exists sufficiently large smaller primitive recursive function

Neil Thapen 1

1 St Hilda's College University of Oxford Oxford OX1 4DY, UK 
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Neil Thapen. A note on $\Delta _1$ induction and $\Sigma _1$ collection. Fundamenta Mathematicae, Tome 186 (2005) no. 1, pp. 79-84. doi : 10.4064/fm186-1-6. http://geodesic.mathdoc.fr/articles/10.4064/fm186-1-6/

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