•Theorem [Furst-Saxe-Sipser, Ajtai] PARITY is not expressible in non-uniform AC0
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•Corollary PARITY is not expressible in FO(All)
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•Comment: i.e. there is no
formula in FO over vocabulary {U} [ All that checks if
|U| is even.
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•Corollary Graph connectivity is not expressible in FO(All)
[why ?]