Universality and Almost Decidability

  title={Universality and Almost Decidability},
  author={Cristian S. Calude and Damien Desfontaines},
We present and study new definitions of universal and program m ble universal unary functions and consider a new simplicity criterion: almost decidability o f the halting set. A set of positive integers S is almost decidable if there exists a decidable and generic (i.e. a set of natural density one) set whose intersection with S is decidable. Every decidable set is almost decidable, but the converse implication is false. We prove the existence of infinitely many universal functions whose… CONTINUE READING

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