Certified $\Sigma_1$-sentences

Taishi Kurahashi; Albert Visser

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arXiv · 2306.13049

Certified $\Sigma_1$-sentences

Taishi Kurahashi·Albert Visser

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Abstract

In this paper, we study the employment of $\Sigma_1$-sentences with certificates, i.e., $\Sigma_1$-sentences where a number of principles is added to ensure that the witness is sufficiently number-like. We develop certificates in some detail and illustrate their use by reproving some classical results and proving some new ones. An example of such a classical result is Vaught's theorem of the strong effective inseparability of $\mathsf{R}_0$. We also develop the new idea of a theory being ${\sf R}_{0{\sf p}}$-sourced. Using this notion, we can transfer a number of salient results from $\mathsf{R}_0$ to a variety of other theories.

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BibTeX RIS

Taishi Kurahashi, Albert Visser. 2023-06-22. Certified $\Sigma_1$-sentences. https://arxiv.org/abs/2306.13049

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