Computability theory was developed by British mathematician Alan
Turing in the 1930s. It was one of the most impactful developments
in mathematics of the 20th century and led to the development of
computers and the modern world.
Admissible sets are mathematical structures generalizing the natural
numbers in which abstract notions of computation is possible. They
are governed by the Kripke-Platek axioms of computability and
possess rich mathematical structure. These abstract forms of
computation relate to usual computation in various ways and help us
understand the limits of computability. They also have applications in
real analysis, game theory, model theory, and descriptive set theory.
This project aims at studying newly discovered kinds of admissible
sets which behave in unexpected ways. Understanding them might
be key in understanding classical admissible sets and could provide
insight into the essence of computation.