The Sandwich Theorems proved in this paper give a new method to show that the partition function a(n) of a partition identity A(x) := ∞ n=0 a(n)x n = ∞ n=1 (1 − x n) −p(n) satisfies the condition RT 1 lim n→∞ a(n − 1) a(n) = 1. This leads to numerous examples of naturally occuring classes of relational structures whose finite members enjoy a logical 0–1 law.
Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions , and their restrictions, have generating series T(z) with a positive radius of convergence; for most of these a simple test can be used to quickly show that the form of the asymptotics is the same as that for… (More)
We determine precisely those locally finite varieties of unary algebras of finite type which, when augmented by a ternary discriminator, generate a variety with a decidable theory.
Characteristic points have been a primary tool in the study of a generating function defined by a single recursive equation. We investigate the proper way to adapt this tool when working with multi-equation recursive systems.
If F(x) = e G(x) , where F(x) = f (n)x n and G(x) = g(n)x n , with 0 ≤ g(n) = O n θn /n! , θ ∈ (0, 1), and gcd n : g(n) > 0 = 1, then f (n) = o(f (n − 1)). This gives an answer to Compton's request in Question 8.3  for an " easily verifiable sufficient condition " to show that an adequate class of structures has a labelled first-order 0–1 law, namely it… (More)
Let F 1 ,. .. , F k be finite fields with distinct characteristics. We give a finite set of equations which axiomatize the equational theory of F 1 ,. .. , F k and then use these axioms to find a finite AC-term rewrite system which is complete for this theory. In particular this gives finite complete AC-term rewrite systems for many instances of x m ≈ x… (More)