Decidable sublanguages of set theory explained

In mathematical logic, various sublanguages of set theory are decidable.^{[1] [2]} These include:

• Sets with Monotone, Additive, and Multiplicative Functions.^[3]
• Sets with restricted quantifiers.^[4]

References

1. 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.
2. http://portal.acm.org/citation.cfm?id=120986.120991&coll=GUIDE&dl=GUIDE&CFID=70880361&CFTOKEN=58203872 "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
3. http://citeseer.ist.psu.edu/cantone03decision.html "A Decision Procedure for a Sublanguage of Set Theory Involving Monotone, Additive, and Multiplicative Functions", by Domenico Cantone and et al.
4. http://turing.dipmat.unict.it/~cantone/p40-97/restrQuant.ps.gz "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