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An Effective Classification of Borel Wadge Classes
Adam Day, Noam Greenberg, Matthew Harrison-Trainor +1
We give a new and effective classification of all Borel Wadge classes of subsets of Baire space. This relies on the true stage machinery originally developed by Montalbán. We use t…
Three topological reducibilities for discontinuous functions
Adam R. Day, Rod Downey, Linda Brown Westrick
We define a family of three related reducibilities, , and , for arbitrary functions , where is a compact separable metric…
Algorithmic Randomness For Amenable Groups
Adam R. Day
We develop the theory of algorithmic randomness for the space where is a finite alphabet and is a computable amenable group. We give an effective version of the Shann…
Density, forcing, and the covering problem
Adam R. Day, Joseph S. Miller
We present a notion of forcing that can be used, in conjunction with other results, to show that there is a Martin-Löf random set X such that X does not compute 0' and X computes e…
From Bi-immunity to Absolute Undecidability
Laurent Bienvenu, Rupert Hölzl, Adam R. Day
An infinite binary sequence A is absolutely undecidable if it is impossible to compute A on a set of positions of positive upper density. Absolute undecidability is a weakening of…
Limits to joining with generics and randoms
Adam R. Day, Damir D. Dzhafarov
Posner and Robinson (1981) proved that if is non-computable, then there exists a such that . Shore and Slaman (1999) extended…