55 citations · 60 across the 5 of their papers we have counts for
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math.LO2003★ 3 cited
The Diagonal Method and Hypercomputation
Toby Ord, Tien D. Kieu
The diagonal method is often used to show that Turing machines cannot solve their own halting problem. There have been several recent attempts to show that this method also exposes…
math.NT2003
Representations of Omega in Number Theory: Finitude Versus Parity
Toby Ord, Tien D. Kieu
We present a new method for expressing Chaitin's random real, Omega, through Diophantine equations. Where Chaitin's method causes a particular quantity to express the bits of Omega…
math.NT2003
On the existence of a new family of Diophantine equations for
Toby Ord, Tien D. Kieu
We show how to determine the -th bit of Chaitin's algorithmically random real number by solving instances of the halting problem. From this we then reduce the problem of…