Computations, Countable Ranks and Complexity of Borel Codes

Explore the intersection of infinite time computation and descriptive set theory in this 37-minute conference talk examining decision times of infinite time algorithms and their relationship to ordinal ranks on subsets of the Cantor space. Learn about the supremum of halting times for real inputs and discover when these ordinals remain countable, with particular focus on results concerning their supremum values. Investigate the converse problem of determining which subsets of the Cantor space admit ranks of countable length at the second level of the Borel hierarchy. Examine the complexity of codes for projective Borel sets without parameters, drawing parallels to Louveau's separation theorem. Gain insights into recent research developments through partial results based on collaborative work with Merlin Carl and Philip Welch, connecting computability theory with higher-order mathematical structures and reverse mathematics principles.