2 Tamara Hummel And
نویسنده
چکیده
We study some generalized notions of cohesiveness which arise naturally in connection with eeective versions of Ram-sey's Theorem. An innnite set A of natural numbers is n{cohesive (respectively, n{r{cohesive) if A is almost homogeneous for every computably enumerable (respectively, computable) 2{coloring of the n{element sets of natural numbers. (Thus the 1{cohesive and 1{r{cohesive sets coincide with the cohesive and r{cohesive sets, respectively.) We consider the degrees of unsolvability and arith-metical deenability levels of n{cohesive and n{r{cohesive sets. For example, we show that for all n 2, there exists a 0 n+1 n{cohesive set. We improve this result for n = 2 by showing that there is a 0 2 2{cohesive set. We show that the n{cohesive and n{r{cohesive degrees together form a linear, non{collapsing hierarchy of degrees for n 2. In addition, for n 2 we characterize the jumps of n{cohesive degrees as exactly the degrees 0 (n+1) and show that each n{r{cohesive degree has jump > 0 (n) .
منابع مشابه
Se p 19 97 GENERALIZED COHESIVENESS
We study some generalized notions of cohesiveness which arise naturally in connection with effective versions of Ram-sey's Theorem. An infinite set A of natural numbers is n–cohesive (respectively, n–r–cohesive) if A is almost homogeneous for every computably enumerable (respectively, computable) 2–coloring of the n–element sets of natural numbers. (Thus the 1–cohesive and 1–r–cohesive sets coi...
متن کاملCALL FOR PAPERS Central Control of Fluid and Electrolyte Homeostasis Characterization of the effects of the vasopressin V2 receptor on sweating, fluid balance, and performance during exercise
Hew-Butler T, Hummel J, Rider BC, Verbalis JG. Characterization of the effects of the vasopressin V2 receptor on sweating, fluid balance, and performance during exercise. Am J Physiol Regul Integr Comp Physiol 307: R366–R375, 2014. First published June 18, 2014; doi:10.1152/ajpregu.00120.2014.—A regulatory effect of arginine vasopressin (AVP) on sweat water conservation has been hypothesized bu...
متن کاملCharacterization of the effects of the vasopressin V 2 receptor 3 on sweating , fluid balance and performance during exercise 4 5 Tamara
39 40 A regulatory effect of arginine vasopressin (AVP) on sweat water conservation has been 41 hypothesized but not definitively evaluated. AVP-mediated insertion of sweat and salivary gland 42 aquaporin-5 (AQP5) water channels through activation of the vasopressin type 2 receptor (V2R) 43 remains an attractive, yet unexplored, mechanism that could result in a more concentrated 44 sweat with r...
متن کاملOn the q-Analogue of the Sum of Cubes
A simple q-analogue of the sum of cubes is given. This answers a question posed in this journal by Garrett and Hummel. The sum of cubes and its q-analogues It is well-known that the first n consecutive cubes can be summed in closed form as n ∑ k=1 k = ( n + 1 2 )2 . Recently, Garrett and Hummel discovered the following q-analogue of this result: n ∑ k=1 qk−1 (1− q)(2− qk−1 − q) (1− q)2(1− q2) =...
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