A CLASSICAL MODAL THEORY OF LAWLESS SEQUENCES

Ethan Brauer
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Abstract

Abstract Free choice sequences play a key role in the intuitionistic theory of the continuum and especially in the theorems of intuitionistic analysis that conflict with classical analysis, leading many classical mathematicians to reject the concept of a free choice sequence. By treating free choice sequences as potentially infinite objects, however, they can be comfortably situated alongside classical analysis, allowing a rapprochement of these two mathematical traditions. Building on recent work on the modal analysis of potential infinity, I formulate a modal theory of the free choice sequences known as lawless sequences. Intrinsically well-motivated axioms for lawless sequences are added to a background theory of classical second-order arithmetic, leading to a theory I call $MC_{LS}$ . This theory interprets the standard intuitionistic theory of lawless sequences and is conservative over the classical background theory.
无规律序列的经典模态理论
自由选择序列在连续统的直觉理论中起着关键的作用,特别是在直觉分析中与经典分析相冲突的定理中,导致许多经典数学家拒绝接受自由选择序列的概念。然而,通过将自由选择序列视为潜在的无限对象,它们可以舒适地与经典分析并列,从而允许这两种数学传统的和解。基于最近对势无穷模态分析的研究,我提出了一种被称为无规律序列的自由选择序列的模态理论。无规律序列的内在良动机公理被添加到经典二阶算法的背景理论中,导致我称之为$MC_{LS}$的理论。这一理论解释了标准的直觉主义的无规律序列理论,并且相对于经典的背景理论是保守的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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