Specker's work on counting labeled finite graphs (in honour of E. Specker's 100th birthday)

In 1981 C. Blatter and E. Specker announced a result on the modular periodicity of combinatorial sequences. They published a proof in 1983 and an expanded version was published by E. Specker as "Application of logic and combinatorics to enumeration problems" in 1988 and is reprinted in the Ernst Specker Selecta of 1990. This is the first application of logic to highly non-trivial combinatorial problems, a meta-theorem anticipating later developments by at least 10 years. I will explain the original result and outline further developments due E. Fischer, T. Kotek and myself.