The ultra-weak Ash conjecture and some particular cases
Annie Château, Malika More · Mathematical logic quarterly · 2005
Ash's functions N σ ,k count the number of k -equivalence classes of σ -structures of size n . Some conditions on their asymptotic behavior imply the long standing spectrum conjecture. We present a new condition which is equivalent to this conjecture and we discriminate some easy and difficult particular cases. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)