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1 Department of Pure Mathematics Waterloo 2 Department of Mathematics and Statistics Boston

Abstract : If Fx = e^Gx, where Fx = \Sum fnx^n and Gx = \Sum gnx^n, with 0 ≤ gn = On^θn-n!, θ ∈ 0,1, and gcdn : gn > 0 = 1, then fn = ofn − 1. This gives an answer to Compton-s request in Question 8.3 Compton 1987 for an -easily verifiable sufficient condition- to show that an adequate class of structures has a labelled first-order 0-1 law, namely it suffices to show that the labelled component count function is On^θn for some θ ∈ 0,1. It also provides the means to recursively construct an adequate class of structures with a labelled 0-1 law but not an unlabelled 0-1 law, answering Compton-s Question 8.4.





Author: Stanley N. Burris - Karen A. Yeats -

Source: https://hal.archives-ouvertes.fr/



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