Examples
Examples of theories that have been shown decidable using quantifier elimination are Presburger arithmetic, algebraically closed fields, real closed fields, atomless Boolean algebras, term algebras, dense linear orders, random graphs, Feature trees, as well as many of their combinations such as Boolean Algebra with Presburger arithmetic, and Term Algebras with Queues. Quantifier elimination can also be used to show that "combining" decidable theories leads to new decidable theories. Such constructions include the Feferman-Vaught theorem and Term Powers.
Read more about this topic: Quantifier Elimination
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