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Model theory of Steiner triple systems
Journal of Mathematical Logic ( IF 0.9 ) Pub Date : 2019-11-12 , DOI: 10.1142/s0219061320500105
Silvia Barbina 1 , Enrique Casanovas 2
Affiliation  

A Steiner triple system (STS) is a set [Formula: see text] together with a collection [Formula: see text] of subsets of [Formula: see text] of size 3 such that any two elements of [Formula: see text] belong to exactly one element of [Formula: see text]. It is well known that the class of finite STS has a Fraïssé limit [Formula: see text]. Here, we show that the theory [Formula: see text] of [Formula: see text] is the model completion of the theory of STSs. We also prove that [Formula: see text] is not small and it has quantifier elimination, [Formula: see text], [Formula: see text], elimination of hyperimaginaries and weak elimination of imaginaries.

中文翻译:

Steiner 三元系统的模型理论

施泰纳三重系统 (STS) 是一个集合 [公式:见文本] 以及 [公式:见文本] 的大小为 3 的子集的集合 [公式:见文本],使得 [公式:见文本] 的任何两个元素恰好属于 [公式:见正文] 的一个元素。众所周知,有限 STS 类具有 Fraïssé 极限[公式:见正文]。在这里,我们证明[公式:见文]的理论[公式:见文]是STS理论的模型补全。我们还证明了【公式:见文】不小,有量词消去、【公式:见文】、【公式:见文】、超想象消去和想象弱消去。
更新日期:2019-11-12
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