The Jump Inversion Theorem for Q 2n+1 -Degrees

1984 ◽  
Vol 90 (3) ◽  
pp. 422
Author(s):  
Ilias G. Kastanas
Keyword(s):  
Inversion Theorem ◽  
Jump Inversion

Almost weakly 2-generic sets

1994 ◽  
Vol 59 (3) ◽  
pp. 868-887 ◽  
Author(s):  
Stephen A. Fenner
Keyword(s):  
Complexity Theory ◽  
Finite Extension ◽  
The Other ◽  
Satisfiability Problem ◽  
Inversion Theorem ◽  
Other Hand ◽  
Jump Inversion ◽  
Generic Set ◽  
Dense Set

AbstractThere is a family of questions in relativized complexity theory—weak analogs of the Friedberg Jump-Inversion Theorem—that are resolved by 1-generic sets but which cannot be resolved by essentially any weaker notion of genericity. This paper defines aw2-generic sets, i.e., sets which meet every dense set of strings that is re. in some incomplete r.e. set. Aw2-generic sets are very close to 1-generic sets in strength, but are too weak to resolve these questions. In particular, it is shown that for any set X there is an aw2-generic set G such that NPG ∩ co-NPG ⊈ PG⊕x. (On the other hand, if G is 1-generic, then NPG ∩ co-NPG ⊆ PG⊕SAT, where SAT is the NP-complete satisfiability problem [6].) This result runs counter to the fact that most finite extension constructions in complexity theory can be made effective. These results imply that any finite extension construction that ensures any of the Friedberg analogs must be noneffective, even relative to an arbitrary incomplete r.e. set. It is then shown that the recursion theoretic properties of aw2-generic sets differ radically from those of 1-generic sets: every degree above 0′ contains an aw2-generic set: no aw2-generic set exists below any incomplete r.e. set: there is an aw2-generic set which is the join of two Turing equivalent aw2-generic sets. Finally, a result of Shore is presented [30] which states that every degree above 0′ is the jump of an aw2-generic degree.

A Jump Inversion Theorem for the Degree Spectra

2009 ◽  
Vol 19 (1) ◽  
pp. 199-215 ◽  
Author(s):  
A. A. Soskova ◽  
I. N. Soskov
Keyword(s):  
Inversion Theorem ◽  
Degree Spectra ◽  
Jump Inversion

scholarly journals An inversion theorem in Fermi surface theory

2000 ◽  
Vol 53 (11) ◽  
pp. 1350-1384 ◽  
Author(s):  
Joel Feldman ◽  
Manfred Salmhofer ◽  
Eugene Trubowitz
Keyword(s):  
Fermi Surface ◽  
Surface Theory ◽  
Inversion Theorem

scholarly journals Strong jump inversion

2018 ◽  
Vol 28 (7) ◽  
pp. 1499-1522
Author(s):  
W Calvert ◽  
A Frolov ◽  
V Harizanov ◽  
J Knight ◽  
C McCoy ◽  
...  
Keyword(s):  
Jump Inversion
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