scholarly journals Interpreting N in the computably enumerable weak truth table degrees

2001 ◽  
Vol 107 (1-3) ◽  
pp. 35-48 ◽  
Author(s):  
André Nies
Keyword(s):  
Truth Table ◽  
Weak Truth Table Degrees ◽  
Computably Enumerable

The theory of the recursively enumerable weak truth-table degrees is undecidable

1992 ◽  
Vol 57 (3) ◽  
pp. 864-874 ◽  
Author(s):  
Klaus Ambos-Spies ◽  
André Nies ◽  
Richard A. Shore
Keyword(s):  
Partial Order ◽  
Open Problem ◽  
Truth Table ◽  
Recursively Enumerable ◽  
Undecidable Theory ◽  
Weak Truth Table Degrees

AbstractWe show that the partial order of -sets under inclusion is elementarily definable with parameters in the semilattice of r.e. wtt-degrees. Using a result of E. Herrmann, we can deduce that this semilattice has an undecidable theory, thereby solving an open problem of P. Odifreddi.

Every incomplete computably enumerable truth-table degree is branching

2001 ◽  
Vol 40 (2) ◽  
pp. 113-123
Author(s):  
Peter A. Fejer ◽  
Richard A. Shore
Keyword(s):  
Truth Table ◽  
Computably Enumerable

On the construction of effectively random sets

2004 ◽  
Vol 69 (3) ◽  
pp. 862-878 ◽  
Author(s):  
Wolfgang Merkle ◽  
Nenad Mihailović
Keyword(s):  
Truth Table ◽  
Random Sets ◽  
Random Set ◽  
Basic Construction ◽  
Computably Enumerable

Abstract.We present a comparatively simple way to construct Martin-Löf random and rec-random sets with certain additional properties, which works by diagonalizing against appropriate martingales. Reviewing the result of Gács and Kučera, for any given set X we construct a Martin-Löf random set from which X can be decoded effectively.By a variant of the basic construction we obtain a rec-random set that is weak truth-table autoreducible and we observe that there are Martin-Löf random sets that are computably enumerable self-reducible. The two latter results complement the known facts that no rec-random set is truth-table autoreducible and that no Martin-Löf random set is Turing-autoreducible [8, 24].

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