11. And, furthermore, are there languages which are not even recursively enumerable ? 12. It is complete but does not have a recursively enumerable set of axioms. 13. From the previous lemma, the set of finitely satisfiable sentences is recursively enumerable . 14. Any axiomatizable fuzzy theory is recursively enumerable . 15. Yuri Matiyasevich utilized a method involving Fibonacci numbers, which computably enumerable set is Diophantine. 16. In general, being recursively enumerable is a weaker condition than being a decidable set. 17. Not every productive set has a recursively enumerable complement, however, as illustrated below. 18. :G�del's incompleteness theorem only applies to proofs based on recursively enumerable axioms. 19. Shore's splitting theorem : Let A be \ alpha recursively enumerable and regular. 20. Let L be a recursively enumerable language.
