皮诺算法片段模型的顺序类型

L. Galeotti, B. Löwe
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引用次数: 0

摘要

Peano算法及其扩展的非标准模型阶型的完全刻画是一个著名的开放问题。在本文中,我们考虑了Peano算术的子理论(包括带归纳和不带归纳),特别是用完整算术语言的适当片段表述的理论。我们研究了它们的非标准模型的阶型,并通过它们可能的阶型来分离所有被考虑的理论。我们比较了有归纳和没有归纳的理论,并观察到没有归纳的理论往往具有代数特征,允许在相关代数操作下通过关闭模型来构建模型。
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ORDER TYPES OF MODELS OF FRAGMENTS OF PEANO ARITHMETIC
Abstract The complete characterisation of order types of non-standard models of Peano arithmetic and its extensions is a famous open problem. In this paper, we consider subtheories of Peano arithmetic (both with and without induction), in particular, theories formulated in proper fragments of the full language of arithmetic. We study the order types of their non-standard models and separate all considered theories via their possible order types. We compare the theories with and without induction and observe that the theories without induction tend to have an algebraic character that allows model constructions by closing a model under the relevant algebraic operations.
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POUR-EL’S LANDSCAPE CATEGORICAL QUANTIFICATION POINCARÉ-WEYL’S PREDICATIVITY: GOING BEYOND A TOPOLOGICAL APPROACH TO UNDEFINABILITY IN ALGEBRAIC EXTENSIONS OF John MacFarlane, Philosophical Logic: A Contemporary Introduction, Routledge Contemporary Introductions to Philosophy, Routledge, New York, and London, 2021, xx + 238 pp.
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