WADGE HIERARCHY Meaning and
Definition
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The Wadge hierarchy is a concept in mathematical logic that describes the classification of certain types of subsets of the real numbers based on their descriptive complexity. Developed by mathematician Stephen Wadge in the early 1980s, the hierarchy aims to categorize sets based on their relative difficulties to describe using formal languages.
In the Wadge hierarchy, a set is considered simpler or less descriptive if it can be defined or approximated by a smaller number of steps or formulas within a given formal system. Sets that can be defined or approximated more easily are said to be at a lower level in the hierarchy, while those that require more complex descriptions are placed at higher levels. The hierarchy is constructed by successively building up sets from simpler ones using various logical operations and techniques.
The Wadge hierarchy has proven to be a useful tool in understanding the descriptive complexity of sets in set theory and other areas of mathematics. It provides a systematic way of comparing and classifying the difficulty of describing different sets in terms of their formal definability or approximability. The hierarchy has also found applications in computer science and theoretical computer science, where it has been used to analyze and classify problems based on their computational complexity.
