41. The question to ask then is : do there exist languages which are recursively enumerable , but not recursive? 42. Similarly, the set of logical consequences of any recursively enumerable set of first-order axioms is semidecidable. 43. The term " enumerable " has the same etymology as in computably enumerable sets of natural numbers. 44. The term " enumerable " has the same etymology as in computably enumerable sets of natural numbers. 45. Recursively enumerable languages are intersection, but not under set difference; see Recursively enumerable language # Closure properties. 46. Recursively enumerable languages are intersection, but not under set difference; see Recursively enumerable language # Closure properties. 47. The theory is assumed to be effective, which means that the set of axioms must be recursively enumerable . 48. Some authors require the class " K " to be definable by a recursively enumerable set of presentations. 49. In 2005 Mayer Goldberg showed that the set of fixed-point combinators of untyped lambda calculus is recursively enumerable . 50. Solomonoff's enumerable measure is universal in a certain powerful sense, but the computation time can be infinite.
