This article needs attention from an expert in mathematics.
mathematical logic, various sublanguages of set theory are decidable.  These include: 
Sets with Monotone, Additive, and Multiplicative Functions.
 Sets with restricted quantifiers.
References [ edit ]
^ Cantone, D., E. G. Omodeo and A. Policriti, "Set Theory for Computing. From Decision Procedures to Logic Programming with Sets," Monographs in Computer Science, Springer, 2001.
^ "Decision procedures for elementary sublanguages of set theory: XIII. Model graphs, reflection and decidability", by Franco Parlamento and Alberto Policriti Journal of Automated Reasoning, Volume 7 , Issue 2 (June 1991), Pages: 271 - 284
^ "A Decision Procedure for a Sublanguage of Set Theory Involving Monotone, Additive, and Multiplicative Functions", by Domenico Cantone and et al.
^ "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