This paper focuses on the categoricity of arithmetic and determinacy of arithmetical truth. Several ‘internal’ categoricity results have been discussed in the recent literature. Against the background of the philosophical position called internalism, we propose and investigate truth-theoretic versions of internal categoricity based on a primitive truth predicate. We argue for the compatibility of a primitive truth predicate with internalism and provide a novel argument for (and proof of) a truth-theoretic version of internal categoricity and internal determinacy with some positive properties.

中文翻译：

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内在范畴性、真理性和确定性

本文主要研究算术的范畴性和算术真理的确定性。最近的文献中讨论了一些“内部”分类结果。在称为内在主义的哲学立场的背景下，我们提出并研究了基于原始真理谓词的内在范畴的真理理论版本。我们主张原始真值谓词与内在主义的兼容性，并为具有某些积极属性的内部范畴性和内部确定性的真值理论版本提供了新颖的论证（和证明） 。