 Yes, there are infinitely many. Kurt Gödel’s incompleteness theorem demonstrated that any system that is strong enough to express arithmetic is also strong enough to express a formal counterpart of the self-referential proposition in the surprise test example ‘This statement cannot be proved in this system’. If the system cannot prove its “Gödel sentence”, then this sentence is true. If the system can prove its Gödel sentence, the system is inconsistent. So either the system is incomplete or inconsistent. (See the entry on  Kurt Gödel.)