A set T has the functions of every predicate for a particular domain. Is a domain of all possible predicates for a domain a finite number because there can't be infinite predicate sentences. I was wondering because if its infinite is it countable or uncountable.
e.g.
Consider the set of predicate logic sentences we can write about the “Possible Missions” domain. Is this set finite; infinite but countable; or not countable? Explain your answer.
My assumption is its finite since there shouldn't be infinite possible missions.
Thanks.