论文标题
与$ \ mathsf {r} $一致的理论的不完整和不确定性
Incompleteness and undecidability of theories consistent with $\mathsf{R}$
论文作者
论文摘要
我们证明了以下版本的第一个不完整定理，同时增强了Mostowski的定理和Vaught的定理：对于任何C.E.一致的tarski，Mostowski和Robinson's Arithmetic $ \ Mathsf {r} $的一致扩展的家庭$ \ { \nvdashφ$和$ t_i \ nvdash \negφ$。
We prove the following version of the first incompleteness theorem that simultaneously strengthens Mostowski's theorem and Vaught's theorem: For any c.e. family $\{ T_i \}_{i \in ω}$ of consistent extensions of Tarski, Mostowski and Robinson's arithmetic $\mathsf{R}$, there exists a sentence $φ$ of arithmetic such that $φ\vdash \mathsf{R}$ and for all $i \in ω$, $T_i \nvdash φ$ and $T_i \nvdash \neg φ$.
