This question is about an answer in question Are there any proofs the undecidability of the halting problem that does not depend on self-referencing or diagonalization ?Bjrn Kjos-Hanssen answer states that:You can first show that the halting problem (the set $0'$) can be used  to compute a set $G\subseteq\mathbb N$ that is 1-generic meaning  that in a sense each $\Sigma^0_1$ fact about $G$ is decided by a  finite prefix of $G$. Then it is easy to prove that such a set $G$  cannot be computable (i.e., decidable).I have trouble understanding this sentence as I am new to forcing. For example, what does finite prefix mean here? Can someone explain this sentence? (I know what $\Sigma^0_1$ means.)Can someone explain the general idea behind forcing? I am also looking for easy to read introductions articles and books about forcing.edit: So, how can we prove that each $\Sigma_1^0$ fact about $G$ being decided by a finite prefix leads to the fact that $G$ cannot be computable?
Explanation of 1-generic to prove undecidability of halting problem
lo.logic;computability;proofs;halting problem