论文标题
相似的模式和bachmann-Howard固定点
Patterns of resemblance and Bachmann-Howard fixed points
论文作者
论文摘要
蒂莫西·卡尔森（Timothy Carlson）的相似模式采用$σ_1$ - elementarity的概念来描述大型可计算序列。已经猜想，这些模式与扩张器的相对化导致与$π^1_1 $ -Comprehension的等价（A.Montalbán的“反向数学中的开放性问题”的问题27，Bull。Symb。Log。17（3）2011，431-454）。在本文中，我们证明了这个猜想。至关重要的方向（朝$π^1_1 $ -COMPERINES）缩小为作者的先前结果，这与Bachmann-Howard Oldinal的相对有关。
Timothy Carlson's patterns of resemblance employ the notion of $Σ_1$-elementarity to describe large computable ordinals. It has been conjectured that a relativization of these patterns to dilators leads to an equivalence with $Π^1_1$-comprehension (Question 27 of A. Montalbán's "Open questions in reverse mathematics", Bull. Symb. Log. 17(3)2011, 431-454). In the present paper we prove this conjecture. The crucial direction (towards $Π^1_1$-comprehension) is reduced to a previous result of the author, which is concerned with relativizations of the Bachmann-Howard ordinal.
