Reducibility orderings: Theories, definability and automorphisms
نویسندگان
چکیده
منابع مشابه
The ∆ 02 Turing degrees : Automorphisms and Definability
We prove that the ∆2 Turing degrees have a finite automorphism base. We apply this result to show that the automorphism group of DT (≤ 0′) is countable and that all its members have arithmetic presentations. We prove that every relation on DT (≤ 0′) induced by an arithmetically definable degree invariant relation is definable with finitely many ∆2 parameters and show that rigidity for DT (≤ 0′)...
متن کاملThe ∆2 Turing Degrees: Automorphisms and Definability
We prove that the ∆2 Turing degrees have a finite automorphism base. We apply this result to show that the automorphism group of DT (≤ 0′) is countable and that all its members have arithmetic presentations. We prove that every relation on DT (≤ 0′) induced by an arithmetically definable degree invariant relation is definable with finitely many ∆2 parameters and show that rigidity for DT (≤ 0′)...
متن کاملDefinability in substructure orderings, IV: finite lattices
Let L be the ordered set of isomorphism types of finite lattices, where the ordering is by embeddability. We study first-order definability in this ordered set. Our main result is that for every finite lattice L, the set {l, l} is definable, where l and l are the isomorphism types of L and its opposite (L turned upside down). We shall show that the only non-identity automorphism of L is the map...
متن کاملDefinability in substructure orderings, I: finite semilattices
We investigate definability in the set of isomorphism types of finite semilattices ordered by embeddability; we prove, among other things, that every finite semilattice is a definable element in this ordered set. Then we apply these results to investigate definability in the closely related lattice of universal classes of semilattices; we prove that the lattice has no non-identical automorphism...
متن کاملDefinability, automorphisms, and dynamic properties of computably enumerable sets
We announce and explain recent results on the computably enumerable (c.e.) sets, especially their definability properties (as sets in the spirit of Cantor), their automorphisms (in the spirit of FelixKlein’sErlanger Programm), their dynamic properties, expressed in terms of how quickly elements enter them relative to elements entering other sets, and theMartin Invariance Conjecture on their Tur...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1980
ISSN: 0003-4843
DOI: 10.1016/0003-4843(80)90004-2