Strong downward Lowenheim Skolem theorems for stationary logics, I
Strong downward Lowenheim Skolem theorems for stationary logics, I
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平稳逻辑的强向下 Lowenheim Skolem 定理，I
DOI：
10.1007/s00153-020-00730-x
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发表时间：
2020
影响因子：
0.3
通讯作者：
Sakai Hiroshi
中科院分区：
文献类型：
--
作者：
Fuchino Sakae;Rodrigues Andre Ottenbreit Maschio;Sakai Hiroshi
本文讨论了带平稳量词的一元（弱）二阶变量扩展一阶逻辑的模型论性质。强向下Löwenheim-Skolem定理（SDLS）的八种变体将二阶变量解释为结构的可数子集，分为四种原则。这四种中最强的一种被证明相当于c和S. Cox内部俱乐部的对角反射原理的结合。我们表明，进一步加强这种SDLS及其变体遵循B. König的博弈反射原则及其推广。
This note concerns the model theoretic properties of logics extending the first-order logic with monadic (weak) second-order variables equipped with the stationarity quantifier. The eight variations of the strong downward Löwenheim–Skolem Theorem (SDLS) down tofor this logic with the interpretation of second-order variables as countable subsets of the structures are classified into four principles. The strongest of these four is shown to be equivalent to the conjunction ofCHand the Diagonal Reflection Principle for internally clubness of S. Cox. We show that a further strengthening of this SDLS and its variations follow from the Game Reflection Principle of B. König and its generalizations.