Abstract
First-order reductions are simple translations that have very little computational power of their own. Thus it is surprising that the vast majority of natural complete problems remain complete via first-order reductions. We provide examples of such complete problems for many complexity classes. All the complexity classes and descriptive languages studied in this book are closed under first-order reductions. Once we express a complete problem for some complexity class C in a language L, it will follow that L contains all queries computable in C.
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