Abraham–Rubin–Shelah open colorings and a large continuum
Abraham–Rubin–Shelah open colorings and a large continuum
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亚伯拉罕·鲁宾·谢拉开放色彩和大连续体
DOI：
10.1142/s0219061321500276
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发表时间：
2022
影响因子：
0.9
通讯作者：
Neeman, Itay
中科院分区：
文献类型：
--
作者：
Gilton, Thomas;Neeman, Itay
我们证明了亚伯拉罕-鲁宾-谢拉开放着色公理与一个大的连续体是一致的，特别是一致的。这回答了[U.Abraham，M.Rubin和S.Shelah]关于连续染色的一些划分定理的一致性以及-稠密实序类型ANN的结构的主要未决问题之一。纯苹果。Logic325(29)(1985)123-206]。正如在[U·亚伯拉罕，M·鲁宾和S·谢拉，关于连续染色的一些划分定理的相合性，以及-稠密实序类型的结构，人工神经网络。纯苹果。Logic325(29)(1985)123-206]，我们需要为所谓的颜色预分配构造名称，以便添加必要的齐次集。然而，已知的预赋值的构造(特别是我们的)只能在假设的情况下工作。为了解决这一困难，我们展示了如何构造具有非常强对称性条件的此类名称。这种对称性允许我们以许多不同的方式将它们结合在一起，使用一种名为分配积的新型偏序集。划分积可以被认为是在存储器上具有严格同构和相干重叠条件的受限存储器迭代。最后，我们构造了配分乘积，它给出了其中的一个模型。
We show that the Abraham–Rubin–Shelah Open Coloring Axiom is consistent with a large continuum, in particular, consistent with. This answers one of the main open questions from [U. Abraham, M. Rubin and S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of-dense real order types,Ann. Pure Appl. Logic325(29) (1985) 123–206]. As in [U. Abraham, M. Rubin and S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of-dense real order types,Ann. Pure Appl. Logic325(29) (1985) 123–206], we need to construct names for the so-calledpreassignments of colorsin order to add the necessary homogeneous sets. However, the known constructions of preassignments (ours in particular) only work assuming the. In order to address this difficulty, we show how to construct such names with very strong symmetry conditions. This symmetry allows us to combine them in many different ways, using a new type of poset called apartition product. Partition products may be thought of as a restricted memory iteration with stringent isomorphism and coherent-overlap conditions on the memories. We finally construct, in, the partition product which gives us a model ofin which.