Topoi also display deep connections to mathematical logic. Every Grothendieck topos has a special sheaf called a subobject classifier. This subobject classifier functions like the set of all possible truth values. In the topos of sets, the subobject classifier is the set formula_11, corresponding to "False" and "True". But in other topoi, the subobject classifier can be much more complicated. Lawvere and Tierney recognized that axiomatizing the subobject classifier yielded a more general kind of topos, now known as an elementary topos, and that elementary topoi were models of intuitionistic logic. In addition to providing a powerful way to apply tools from logic to geometry, this made possible the use of geometric methods in logic.