Hyperarithmetical Sets
The central focus of hyperarithmetic theory are certain sets of natural numbers known as hyperarithmetic sets. There are three equivalent ways of defining this class of sets; the study of the relationships between these different definitions is one motivation for the study of hyperarithmetical theory.
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“It is mediocrity which makes laws and sets mantraps and spring-guns in the realm of free song, saying thus far shalt thou go and no further.”
—James Russell Lowell (181991)