FROM BOUNDED ARITHMETIC TO SECOND ORDER ARITHMETIC VIA AUTOMORPHISMS
FROM BOUNDED ARITHMETIC TO SECOND ORDER ARITHMETIC VIA AUTOMORPHISMS
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通过自同构从有界算术到二阶算术
DOI：
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发表时间：
2005
期刊：
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通讯作者：
A. Enayat
中科院分区：
文献类型：
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作者：
A. Enayat
在本文中，我们研究了模型的自同构的有界算术和强系统的算术，如PA，ACA 0（算术理解模式与限制归纳），和Z2（二阶算术）之间的关系。例如，我们通过证明Gaifman定理的“反转”来建立PA的以下特征：定理。对于I <$0的完备化T，下列结果是等价的：（a）T ` PA;（B）T的某个模型M =（M，· · ·）有一个适当的端扩张N满足I <$0，并且对于N的某个自同构j，M恰好是j的不动点集.我们的结果还揭示了具有泛集的集合论Quine-Jensen系统NFU的元数学.
In this paper we examine the relationship between automorphisms of models of I∆0 (bounded arithmetic) and strong systems of arithmetic, such as PA, ACA0 (arithmetical comprehension schema with restricted induction), and Z2 (second order arithmetic). For example, we establish the following characterization of PA by proving a “reversal” of a theorem of Gaifman: Theorem. The following are equivalent for completions T of I∆0 : (a) T ` PA; (b) Some model M = (M, · · ·) of T has a proper end extension N which satisfies I∆0 and for some automorphism j of N, M is precisely the fixed point set of j. Our results also shed light on the metamathematics of the Quine-Jensen system NFU of set theory with a universal set.