Jump Embeddings in the Turing Degrees
نویسندگان
چکیده
Much of the work on Turing degrees may be formulated in terms of the embeddability of certain first-order structures in a structure whose universe is some set of degrees and whose relations, functions, and constants are natural degree-theoretic ones. Thus, for example, we know that if (P, ≤P ) is a partial ordering of cardinality at most א1 which is locally countable—each point has at most countably many predecessors—then there is an embedding
منابع مشابه
On the Symmetric Enumeration Degrees
A set A is symmetric enumeration (se-) reducible to a set B (A≤seB) if A is enumeration reducible to B and A is enumeration reducible to B. This reducibility gives rise to a degree structure (Dse) whose least element is the class of computable sets. We give a classification of ≤se in terms of other standard reducibilities and we show that the natural embedding of the Turing degrees (DT) into th...
متن کاملGoodness in the enumeration and singleton degrees
We investigate and extend the notion of a good approximation with respect to the enumeration (De) and singleton (Ds) degrees. We refine two results by Griffith, on the inversion of the jump of sets with a good approximation, and we consider the relation between the double jump and index sets, in the context of enumeration reducibility. We study partial order embeddings ιs and ι̂s of, respectivel...
متن کاملComputability, Traceability and Beyond
This thesis is concerned with the interaction between computability and randomness. In the first part, we study the notion of traceability. This combinatorial notion has an increasing influence in the study of algorithmic randomness. We prove a separation result about the bounds on jump traceability, and show that the index set of the strongly jump traceable computably enumerable (c.e.) sets is...
متن کاملExtensions of Embeddings below Computably Enumerable Degrees
Toward establishing the decidability of the two quantifier theory of the ∆ 2 Turing degrees with join, we study extensions of embeddings of upper-semi-lattices into the initial segments of Turing degrees determined by computably enumerable sets, in particular the degree of the halting set 0. We obtain a good deal of sufficient and necessary conditions.
متن کاملGlobal Properties of the Turing Degrees and the Turing Jump
We present a summary of the lectures delivered to the Institute for Mathematical Sciences, Singapore, during the 2005 Summer School in Mathematical Logic. The lectures covered topics on the global structure of the Turing degrees D, the countability of its automorphism group, and the definability of the Turing jump within D.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006