论文标题
基本的遗传性不可证明
Essential Hereditary Undecidability
论文作者
论文摘要
在本文中，我们研究\ emph {基本的遗传性不可证明}。具有此属性的理论是证明其他理论不可证明的方便工具。本文开发了有关遗传性不可证实的基本事实，并提供了显着的例子，例如由于HANF而建立的\ ehu \理论的构造，以及一个基本上基本上基本上不可决定的理论的示例，严格在{\ sf r}以下。我们讨论基本遗传性不可证明与递归布尔同构的（非）相互作用。 我们开发了一个还原关系\ emph {基本公差}，或者，在相反的方向上，\ emph {lax dycrybility}与基本的遗传性不可证明性很好地相互作用。 我们介绍了$σ^0_1 $ - 友好的理论的类别，并表明$σ^0_1 $ - 友谊足够，但对于基本的遗传性不可证明是不需要的。 最后，我们根据Pakhomov，Murwanashyaka和Visser适应了一个论点，以表明没有解释性最小的基本上是遗传性的理论。
In this paper we study \emph{essential hereditary undecidability}. Theories with this property are a convenient tool to prove undecidability of other theories. The paper develops the basic facts concerning essentially hereditary undecidability and provides salient examples, like a construction of \ehu\ theories due to Hanf and an example of a rather natural essentially hereditarily undecidable theory strictly below {\sf R}. We discuss the (non-)interaction of essential hereditary undecidability with recursive boolean isomorphism. We develop a reduction relation \emph{essential tolerance}, or, in the converse direction, \emph{lax interpretability} that interacts in a good way with essential hereditary undecidability. We introduce the class of $Σ^0_1$-friendly theories and show that $Σ^0_1$-friendliness is sufficient but not necessary for essential hereditary undecidability. Finally, we adapt an argument due to Pakhomov, Murwanashyaka and Visser to show that there is no interpretability minimal essentially hereditarilyundecidable theory.
