decidable

adjective

de·​cid·​able di-ˈsī-də-bəl 

: capable of being decided

specifically : capable of being decided as following or not following from the axioms of a logical system

Was logic complete … ? And was it decidable, in the sense that there was a method that demonstrated the truth or falsity of every statement?

—Stan Augarten

By the beginning of this century symbolic logic had progressed to such an extent that the German mathematician David Hilbert declared that all mathematical questions are in principle decidable …

—Gregory J. Chaitin

decidability

di-ˌsī-də-ˈbi-lə-tē 

noun

Word History

Etymology

decide + -able

First Known Use

1594, in the meaning defined above