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A non-splitting theorem for d.r.e. sets
1996
Annals of Pure and Applied Logic
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Sacks showed that for each non-recursive recursively enumerable set A there are disjoint recursively enumerable sets B, C which cover A such that A is recursive in neither A n B nor A n C. ...
Abstract A set of natural numbers is called d.r.e. ...
There exists a properly d.r.e. set D such that for all r.e. sets AO, A1 with A0 n A1 = 0, D~A O U A~~[ D <~A O~D V D <~A~~D ] .
r 6 3 ' 3 J, for all j E {jo,. ...
doi:10.1016/0168-0072(95)00070-4
fatcat:enkgzixxwreqbawb7n66q3a3fq
Page 5961 of Mathematical Reviews Vol. , Issue 97J
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1997
Mathematical Reviews
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This is in contrast to Sacks’s splitting theorem for re. sets. ...
Peter Cholak (1-NDM; Notre Dame, IN)
03D Recursion theory
97}:03089
97j:03086 03D30 03D25
Yi, Xiaoding (1-CT; Storrs, CT)
A non-splitting theorem for d.r.e. sets. (English summary)
Ann. Pure Appl. ...
Recursively enumerable sets and degrees
1978
Bulletin of the American Mathematical Society
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The structure, automorphisms, and elementary theory of the r.e. sets. 6. Basic facts and splitting theorems. 7. Hh-simple sets. 8. Major subsets and r-maximal sets. 9. Automorphisms of &. 10. ...
A subset A of <o (the set of nonnegative integers) is recursive (also called decidable or computable) if there is an algorithm for determining whether a ...
SETS 6. Basic facts and splitting theorems. ...
doi:10.1090/s0002-9904-1978-14552-2
fatcat:arxp4btvhzfzjeoufybmnemt2u
Master index to volumes 61-70
1994
Annals of Pure and Applied Logic
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Jin, R. and Shelah, S., Essential Kurepa trees versus essential Jech-Kunen trees Joyal, A. and Moerdijk, I., A completeness theorem for open maps Kaddah, D., Infima in the d.r.e. degrees Kagan, V., Nerode ...
with non-constructive p-operator. ...
doi:10.1016/s0168-0072(94)90013-2
fatcat:jcewrks7xbf4peme3526yoypre
d-simple sets, small sets, and degree classes
1980
Pacific Journal of Mathematics
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Thus ^iCΰ and D splits L u and likewise for D replaced by N, the degrees containing non-small sets. We do not know whether D^L λ or whether N -D. THEOREM 4.1. ...
The construction is very similar to the usual construction [18, Theorem 4.1] of a low simple set A except that A must now intersect certain infinite d.r.e. sets instead of certain infinite r.e. sets. ...
doi:10.2140/pjm.1980.87.135
fatcat:xilieu56zbh7fi57s2wg3bbyxa
The index set of uncountably categorical theories
2013
Israel Journal of Mathematics
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We show that this index set surprisingly falls at the intermediate stage of being complete for intersections of Π 2 sets with Σ 2 sets. ...
We classify the complexity of the index set of uncountably categorical theories. ...
Surprisingly, uncountable categoricity is arithmetical and lies at an intermediate level, being complete for intersections of a Π 2 set and a Σ 2 set (also known as 0 -d.r.e. sets). ...
doi:10.1007/s11856-013-0011-1
fatcat:3ficgnd3v5dy5lq3siqgy7miwi
On α- and β-recursively enumerable degrees
1979
Annals of Mathematical Logic
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In particular by applying the splitting theorem to many local structures we get a global splitting theorem for all regular /3-r.e. degrees. ...
It turns out that routine precautions are sufficient to make the proof work for all admissible structures. Call a set D 9l-d.r.e. if D = A -B for some ')l-r e. sets A. B. ...
doi:10.1016/0003-4843(79)90002-0
fatcat:kaew2ei5gjgb7p4g76ba277uly
On the Turing Degrees of Weakly Computable Real Numbers
2003
Journal of Logic and Computation
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The Turing degree of a real number x is defined as the Turing degree of its binary expansion. This definition is quite natural and robust. ...
Therefore, every non-computable c.e. degree contains both semi-computable and non-semi-computable real numbers. Theorem 1.7 For any non-computable c.e. ...
By Sacks' Splitting Theorem [14] there exist two incomparable c.e. degrees b 0 , b 1 such that a = b 0 ∪ b 1 . Choose two c.e. sets B 0 ∈ b 0 and B 1 ∈ b 1 and define set A =: B 0 ⊕ B 1 . ...
doi:10.1093/logcom/13.2.159
fatcat:4lp67kl5vvh2tpphr53gxt4w6e
Page 96 of Mathematical Reviews Vol. , Issue Index
[page]
Mathematical Reviews
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theorem for d.r.e. sets. ...
(English summary) 971:03026
— (with Sui, Yuefei) An extended Lachlan splitting theorem. (English summary) 97b:03055
— see also Arsianov, M. ...
Page 104 of Mathematical Reviews Vol. , Issue Index
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Mathematical Reviews
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(English summary) 98c:03092
Kontostathis, Kyriakos The combinatorics of the splitting theorem. 98j:03059
Kumabe, Masahiro Minimal complementation below uniform upper bounds for the arithmetical degrees ...
03D25
03D25 Recursively enumerable sets and degrees
Cichon, E. A. (with Weiermann, Andreas) Term rewriting theory for the primitive recursive functions. (English summary) 98b:03057
Cooper, S. ...
2015 EUROPEAN SUMMER MEETING OF THE ASSOCIATION FOR SYMBOLIC LOGIC LOGIC COLLOQUIUM '15 Helsinki, Finland August 3–8, 2015
2016
Bulletin of Symbolic Logic
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, or a set of assignments. ...
In set theory, a reflection principle says that a proposition true in the universe holds already in a smaller set. ...
We prove that for some sequence of tautologies ϕn the proof steps and the proof sizes in ...
doi:10.1017/bsl.2016.22
fatcat:cm4a5yyvgfajzm4qvlszviblni
Page 110 of Mathematical Reviews Vol. 32, Issue Index
[page]
Mathematical Reviews
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Maximal sets and the jump operator. 2000a:03065
Ding, Decheng see Lu, Hong et al., 2000f:03123 and 2000m:03100
Downey, Rodney G. (with Shore, Richard A.) Splitting theorems and the jump operator. ...
Arslanov, Asat Difference splittings of recursively enumerable sets. ...
Page 90 of Mathematical Reviews Vol. 27, Issue Index
[page]
Mathematical Reviews
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(English summary) 95h:03103
Splitting theorems in recursion theory. (English
Highness and bounding minimal pairs.
with Kummer, Martin Walter) Diagonals and ®-maximal sets. ...
(with Yi, Xiaoding) Jump theorems for REA operators. (English summary) 95b:03048
Morales-Luna, Guillermo Degrees of complexity of recursive functions and degrees of unsolvability. (Spanish. ...
Page 1638 of Mathematical Reviews Vol. , Issue Index
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Mathematical Reviews
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(Peter Cholak) 97e:03063 03D25
— A non-splitting theorem for d.r.e. sets. (English summary) Ann. Pure Appl. Logic 82 (1996), no. 1, 17-96. ...
(see 97a:90003) 93E20 (90B70, 90C40)
— (with Zhang, Qing') A central limit theorem for singularly perturbed nonstationary finite state Markov chains. (English summary) Ann. Appl. ...