Model theory of Steiner triple systems
Keyword(s):
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.
2010 ◽
Vol 62
(2)
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pp. 355-381
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1983 ◽
Vol 94
(1-2)
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pp. 89-92
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1974 ◽
Vol 26
(1)
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pp. 225-232
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1975 ◽
Vol 27
(2)
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pp. 256-260
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Keyword(s):
1976 ◽
Vol 28
(6)
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pp. 1187-1198
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Keyword(s):
2014 ◽
Vol 513-517
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pp. 2995-2998
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