Computability in Europe 2006
Logical Approaches to Computational Barriers
|THIS TALK HAS BEEN CANCELLED!!!|
The theory of hypercomputation aims to extend effective computability beyond Turing reducibility, in particular by means of supertasks; physical models are considered in Newtonian, relativistic and quantum contexts. Apart from implementation differences, all approaches take for granted that supertask computations would decide arithmetic; in logical terms, this amounts to assume that the undecidability of Peano Arithmetic can be bypassed by the omega-rule. We argue that this assumption is untenable, as long as the system is consistent: the conclusion follows from alternative versions of Gödelís incompleteness, such as Rosserís and Yabloís, which are indifferent to infinite deductions.
|websites: Arnold Beckmann||
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