回避与预测--斯派克现象与格罗斯空间
Evasion and prediction --- the Specker phenomenon and Gross spaces
摘要：
我们研究了以下两个代数现象的集合论组合数学。(1)子群G leq Z^omega表现出Specker现象当且仅当每个同态G到Z映射几乎所有单位向量到0。设se是表现出斯派克现象的最小G leq Z^ω的大小。(2)给定一个至多可数域KK上的不可数维向量空间E，E具有对称双线性型Phi，（E，Phi）是强Gross当且仅当对所有可数维U leq E，我们有dim（U^perp）leq Ω.布拉斯指出，斯派克现象与一种他称之为回避和预测的组合现象密切相关。我们证明了几个额外的结果（ZFC定理和独立性证明）逃避和预测以及SE，并涉及一个Luzin-风格的财产与逃避强格罗斯空间的存在。
英文摘要：
We study the set--theoretic combinatorics underlying the following two algebraic phenomena. (1) A subgroup G leq Z^omega exhibits the Specker phenomenon iff every homomorphism G to Z maps almost all unit vectors to 0. Let se be the size of the smallest G leq Z^omega exhibiting the Specker phenomenon. (2) Given an uncountably dimensional vector space E equipped with a symmetric bilinear form Phi over an at most countable field KK, (E,Phi) is strongly Gross iff for all countably dimensional U leq E, we have dim(U^perp) leq omega. Blass showed that the Specker phenomenon is closely related to a combinatorial phenomenon he called evading and predicting. We prove several additional results (both theorems of ZFC and independence proofs) about evading and predicting as well as se, and relate a Luzin--style property associated with evading to the existence of strong Gross spaces.
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