Transfer and a supremum principle for ERNA
Transfer and a supremum principle for ERNA
复制标题
ERNA 的转移和最高原则
DOI：
10.2178/jsl/1208359067
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发表时间：
2008
影响因子：
0.6
通讯作者：
Sam Sanders
中科院分区：
文献类型：
--
作者：
C. Impens;Sam Sanders
摘要初等递归非标准分析（Elementary Recursive Nonstandard Analysis，简称ERNA）是帕特里克·苏佩斯（Patrick Suppes）和理查德·索默（Richard Sommer）于1995年左右提出的一个非标准分析的构造性系统，并在PRA中证明了它的一致性。它基于Rolando Chuaqui和帕特里克Suppes开发的早期系统，Michal Rössler和Emil Jeanábek最近提出了一个弱化版本。我们在ERNA中加入了一个能量转移原理，并证明了扩展理论在PRA中的一致性。在ERNA的这种扩展中，推导出了一个上确界原理“直到无穷小”，以及一些著名的序列微积分结果。最后，我们通过重新考虑Rössler和Jeanábek的结论，证明了转移对于有限论来说“太强了”。
Abstract Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis proposed around 1995 by Patrick Suppes and Richard Sommer, who also proved its consistency inside PRA. It is based on an earlier system developed by Rolando Chuaqui and Patrick Suppes, of which Michal Rössler and Emil Jeřábek have recently proposed a weakened version. We add a Πı-transfer principle to ERNA and prove the consistency of the extended theory inside PRA. In this extension of ERNA a Σı-supremum principle ‘up-to-infinitesimals’, and some well-known calculus results for sequences are deduced. Finally, we prove that transfer is ‘too strong’ for finitism by reconsidering Rössler and Jeřábek's conclusions.