mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

, various sublanguages of

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...

are decidable. These include: * Sets with Monotone, Additive, and Multiplicative Functions. * Sets with restricted quantifiers."A tableau-based decision procedure for a fragment of set theory involving a restricted form of quantification", by Domenico Cantone, Calogero G. Zarba, Viale A. Doria, 1997
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References

Proof theory Logic in computer science Model theory