Asymptotic classes of finite structures
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In this paper we consider classes of finite structures where we have good control over the sizes of the definable sets. The motivating example is the class of finite fields: it was shown in [1] that for any formula in the language of rings, there are finitely many pairs (d, μ) ∈ ω × Q>0 so that in any finite field F and for any ā ∈ Fm the size |ø(Fn,ā)| is “approximately” μ|F|d. Essentially this is a generalisation of the classical Lang-Weil estimates from the category of varieties to that of the first-order-definable sets.
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2012 ◽
Vol 55
(2)
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pp. 418-423
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2003 ◽
Vol 55
(2)
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pp. 225-246
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2020 ◽
Vol 31
(03)
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pp. 411-419
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2016 ◽
Vol 12
(06)
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pp. 1519-1528
1982 ◽
Vol 34
(2)
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pp. 500-505
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