论文标题
没有最小的有效分离理论
There are no minimal effectively inseparable theories
论文作者
论文摘要
本文属于关于第一个不完整定理极限的研究。有效地不可分割的理论（EI）可以看作是本质上不确定的理论（EU）的有效版本，而EI比欧盟强。我们研究了一个问题：关于解释性，是否有效地不可分割的理论有效。我们提出了TEI，这是EI的理论版本。我们首先证明没有关于可解释性的最小TEI理论（即，对于任何TEI理论$ t $，我们可以有效地找到一种TEI和严格弱于$ t $的理论。根据Marian B. Pour-ei的定理，我们的TEI与EI相当。因此，关于解释性没有最小的EI理论。我们还证明，对于解释性，没有最少有限的公理EI理论。
This paper belongs to the research on the limit of the first incompleteness theorem. Effectively inseparable theories (EI) can be viewed as an effective version of essentially undecidable theories (EU), and EI is stronger than EU. We examine the question: are there minimal effectively inseparable theories with respect to interpretability. We propose tEI, the theory version of EI. We first prove that there are no minimal tEI theories with respect to interpretability (i.e., for any tEI theory $T$, we can effectively find a theory which is tEI and strictly weaker than $T$ with respect to interpretability). By a theorem due to Marian B. Pour-EI, we have tEI is equivalent with EI. Thus, there are no minimal EI theories with respect to interpretability. Also we prove that there are no minimal finitely axiomatizable EI theories with respect to interpretability.
