强制作为访问小型扩展的本地方法

arXiv - MATH - Logic Pub Date : 2024-09-05 DOI:arxiv-2409.03441

Desmond Lau

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引用次数: 0

摘要

固定一个集合论宇宙 $V$。我们把 $V$ 的小扩展看作 $V$ 上的广义可计算性度。我们还形式化并研究了某些方法的复杂性，这些方法可以用来在 $V$ 中定义 $V$ 上的度的子类。最后，我们给出了在这个框架内强迫的复杂性的一个很好的表征。

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Forcing as a Local Method of Accessing Small Extensions

Fix a set-theoretic universe $V$. We look at small extensions of $V$ as generalised degrees of computability over $V$. We also formalise and investigate the complexity of certain methods one can use to define, in $V$, subclasses of degrees over $V$. Finally, we give a nice characterisation of the complexity of forcing within this framework.

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arXiv - MATH - Logic

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