Abstract
This chapter provides an overview of some applications of the notions of forcing and generic sets. The notions of forcing and of generic sets were introduced by Paul Cohen [*] to settle long-outstanding logical independence problems relative to Zermelo-Fraenkel set theory. This chapter explains these notions to other contexts, namely that of number theory and analysis, and obtain applications there as well as some new applications in set theory. The definition is to be regarded as being further supplemented to take care of higher-order languages. However, the only change for these cases is to bring in additional clauses for the higher-order existential quantifiers. To prove the independence of the axiom of choice, Cohen [*] introduced certain symmetries into the model he constructed by considering permutations π of ω.
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