I understand following about recognizable (aka recursively enumerable) and co-recognizable languages:
Definition 1: Recognizable language is one which have one-to-one correspondence with the natural number with the additional property that we could specify an algorithm to enumerate the language elements.
For recognizable language, we can specify Turing machine which can enumerate the language elements.
Given the string in the recognizable language, Turing machine can eventually confirm that the string indeed belongs to the language.
Language L is called co-Turing-recognizable, if L’ is Turing-recognizable.
Given the string not in the co-recognizable language, Turing machine can eventually confirm that the string indeed does not belong to the language.
Q1. What is definition 1 equivalent of co-recognizable languages?
Q2. Do they also have one-to-one correspondence to natural numbers?
Q3. Do they also have Turing machine associated with them which can enumerate their elements?
Q4. If answer to Q2 and Q3 is true, then doesnt it make them same as recognizable?