<> "The repository administrator has not yet configured an RDF license."^^ . <> . . "Multiple Permitting and Bounded Turing Reducibilities"^^ . "We look at various properties of the computably enumerable (c.e.) not totally ω-c.e. Turing degrees.\r\nIn particular, we are interested in the variant of multiple permitting given by those degrees. We\r\ndefine a property of left-c.e. sets called universal similarity property which can be viewed as a\r\nuniversal or uniform version of the property of array noncomputable c.e. sets of agreeing with any\r\nc.e. set on some component of a very strong array. Using a multiple permitting argument, we\r\nprove that the Turing degrees of the left-c.e. sets with the universal similarity property coincide\r\nwith the c.e. not totally ω-c.e. degrees. We further introduce and look at various notions of socalled\r\nuniversal array noncomputability and show that c.e. sets with those properties can be found\r\nexactly in the c.e. not totally ω-c.e. Turing degrees and that they guarantee a special type of\r\nmultiple permitting called uniform multiple permitting. We apply these properties of the c.e. not\r\ntotally ω-c.e. degrees to give alternative proofs of well-known results on those degrees as well as\r\nto prove new results. E.g., we show that a c.e. Turing degree contains a left-c.e. set which is not\r\ncl-reducible to any complex left-c.e. set if and only if it is not totally ω-c.e. Furthermore, we prove\r\nthat the nondistributive finite lattice S7 can be embedded into the c.e. Turing degrees precisely\r\nbelow any c.e. not totally ω-c.e. degree.\r\nWe further look at the question of join preservation for bounded Turing reducibilities r and r′\r\nsuch that r is stronger than r′. We say that join preservation holds for two reducibilities r and\r\nr′ if every join in the c.e. r-degrees is also a join in the c.e. r′-degrees. We consider the class of\r\nmonotone admissible (uniformly) bounded Turing reducibilities, i.e., the reflexive and transitive\r\nTuring reducibilities with use bounded by a function that is contained in a (uniformly computable)\r\nfamily of strictly increasing computable functions. This class contains for example identity bounded\r\nTuring (ibT-) and computable Lipschitz (cl-) reducibility. Our main result of Chapter 3 is that join\r\npreservation fails for cl and any strictly weaker monotone admissible uniformly bounded Turing\r\nreducibility. We also look at the dual question of meet preservation and show that for all monotone\r\nadmissible bounded Turing reducibilities r and r′ such that r is stronger than r′, meet preservation\r\nholds. Finally, we completely solve the question of join and meet preservation in the classical\r\nreducibilities 1, m, tt, wtt and T."^^ . "2018" . . . . . . . "Losert"^^ . "Nadine"^^ . "Losert Nadine"^^ . . . . . . "Multiple Permitting and Bounded Turing Reducibilities (PDF)"^^ . . . "diss.pdf"^^ . . . "Multiple Permitting and Bounded Turing Reducibilities (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "Multiple Permitting and Bounded Turing Reducibilities (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Multiple Permitting and Bounded Turing Reducibilities (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Multiple Permitting and Bounded Turing Reducibilities (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Multiple Permitting and Bounded Turing Reducibilities (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #24241 \n\nMultiple Permitting and Bounded Turing Reducibilities\n\n" . "text/html" . . . "004 Informatik"@de . "004 Data processing Computer science"@en . . . "510 Mathematik"@de . "510 Mathematics"@en . .