文章基本信息

标题：On the Arithmetical Content of Restricted Forms of Comprehension, Choice and General Uniform Boundedness
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作者：Ulrich Kohlenbach
期刊名称：BRICS Report Series
印刷版ISSN：0909-0878
出版年度：1997
卷号：4
期号：23
出版社：Aarhus University
摘要：In this paper the numerical strength of fragments of arithmetical comprehension, choice and general uniform boundedness is studied systematically. These principles are investigated relative to base systems Tn^omega in all finite types which are suited to formalize substantial parts of analysis but nevertheless have provably recursive function(al)s of low growth. We reduce the use of instances of these principles in Tn^omega -proofs of a large class of formulas to the use of instances of certain arithmetical principles thereby determining faithfully the arithmetical content of the former. This is achieved using the method of elimination of Skolem functions for monotone formulas which was introduced by the author in a previous paper. As corollaries we obtain new conservation results for fragments of analysis over fragments of arithmetic which strengthen known purely first-order conservation results.