弗协调控制收敛
Paraconsistent Dominated Convergence
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中文总结 AI 辅助
本文将形式洛朗级数的列维-奇维塔域的积分理论嵌入弗协调框架并扩展到测度理论，通过源分块与目标分块及渗透关系得出经典勒贝格控制收敛定理，证明弗协调逻辑可为分析工具提供基础并限制不一致性。
中文摘要 AI 辅助
形式洛朗级数的列维-奇维塔域$\mathcal{R}$是一个构造性的、非阿基米德有序域，它支持完整的勒贝格测度和积分理论，包括控制收敛定理。本文将该积分理论嵌入到弗协调的分块与渗透框架中，将其从初等微积分扩展到真正的测度理论。源分块由具有其测度和积分的$\mathcal{R}$建模，而目标分块是经典实数线$\mathbb{R}$。一个渗透关系输出内部积分的标准部分，并且证明了控制收敛定理从源分块渗透到目标分块，得到经典的勒贝格控制收敛定理，无需任何选择原则，也无需非标准测度理论所需的超滤子。该构造完全明确，表明弗协调逻辑可以为深入的分析工具提供严格的基础，同时将不一致性安全地限制在一定范围内。
英文摘要
The Levi-Civita field $\mathcal{R}$ of formal Laurent series is a constructive, non-Archimedean ordered field that supports a full Lebesgue measure and integration theory, including a Dominated Convergence Theorem. This paper embeds that integration theory into the paraconsistent Chunk and Permeate framework, extending it from elementary calculus to genuine measure theory. The source chunk is modelled by $\mathcal{R}$ with its measure and integral, while the target chunk is the classical real line $\mathbb{R}$. A permeability relation exports the standard part of the internal integral, and it is shown that the Dominated Convergence Theorem permeates from the source chunk to the target chunk, yielding the classical Lebesgue Dominated Convergence Theorem without any choice principles and without the ultrafilters required by nonstandard measure theory. The construction is entirely explicit and demonstrates that paraconsistent logic can provide a rigorous foundation for deep analytical tools while keeping inconsistencies safely confined.
