论文标题
在三个要素的更好的准顺序的逻辑强度上
On the logical strength of the better quasi order with three elements
论文作者
论文摘要
由于纳什·威廉姆斯（Nash-Williams），从逻辑的角度来看，由于纳什·威廉姆斯（Nash-Williams）的纳什·威廉姆斯（Nash-Williams），由于纳什·威廉姆斯（Nash-Williams）而引起的概念非常富有成果，而且由于几个长期的开放问题，因此在数学上非常富有成果。在本文中，我们迈出了重要的一步：让$ \ mathbf 3 $是带有三个元素的离散订单。我们表明，沿自然数（$ \ mathsf {aca} _0^+$）沿着$ \ mathbf 3 $为$ \ mathsf {bqo} $沿着基本理论$ \ mathsf {rca_0} $从反向数学来看。同样，在后者的情况下，我们从假设$ \ Mathbf 3 $是$Δ^0_2 \ text { - } \ Mathsf {bqo} $的假设中推断出算术递归递归（$ \ Mathsf {atr} _0 $），该递归是$ \ Mathbf { - } \ text { - } \ mathsf {bqo} $，在Montalbán的工作中扮演角色。
The notion of better quasi order ($\mathsf{BQO}$), due to Nash-Williams, is very fruitful mathematically and intriguing from the standpoint of logic, due to several long-standing open problems. In the present paper, we make a significant step towards one of these: Let $\mathbf 3$ be the discrete order with three elements. We show that arithmetical recursion along the natural numbers ($\mathsf{ACA}_0^+$) follows from $\mathbf 3$ being $\mathsf{BQO}$, over the base theory $\mathsf{RCA_0}$ from reverse mathematics. Also over the latter, we deduce arithmetical transfinite recursion ($\mathsf{ATR}_0$) from the assumption that $\mathbf 3$ is $Δ^0_2\text{-}\mathsf{BQO}$, which plays a role in work of Montalbán.
