Separating families and order dimension of Turing degrees
作者： Ashutosh Kumar , Dilip Raghavan
DOI: 10.1016/J.APAL.2020.102911
关键词: Continuum (topology) 、 Turing 、 Order dimension 、 Mathematics 、 Countable set 、 Pure mathematics
摘要: Abstract We study families of functions and linear orders which separate countable subsets the continuum from points. As an application, we show that order dimension Turing degrees, denoted dim T , cannot be decided in ZFC. also provide a combinatorial description degrees have largest among all locally partial size continuum. Finally, prove it is consistent number needed to points strictly smaller than necessary for separating them.
sci-hub.st 参考文章(13)
Henry Kierstead, E. C. Milner, The dimension of the finite subsets κ Order. ,vol. 13, pp. 227- 231 ,(1996) , 10.1007/BF00338742
K. Kunen, Weak P-Points in N* Birkhäuser Basel. pp. 100- 108 ,(1993) , 10.1007/978-3-0348-7524-0_10
Stevo Todorcevic, Walks on ordinals and their characteristics ,(2007)
Stevo Todorčevič, Reals and Positive Partition Relations Studies in Logic and the Foundations of Mathematics. ,vol. 114, pp. 159- 169 ,(1986) , 10.1016/S0049-237X(09)70691-3
Stevo Todorcevic, Partition relations for partially ordered sets Acta Mathematica. ,vol. 155, pp. 1- 25 ,(1985) , 10.1007/BF02392535
Marcia J. Groszek, Theodore A. Slaman, Independence results on the global structure of the Turing degrees Transactions of the American Mathematical Society. ,vol. 277, pp. 579- 588 ,(1983) , 10.1090/S0002-9947-1983-0694377-4
Kenneth Kunen, Set Theory: An Introduction to Independence Proofs ,(2011)
James E. Baumgartner, Almost disjoint sets, the dense set problem and the partition calculus Annals of Mathematical Logic. ,vol. 9, pp. 401- 439 ,(1976) , 10.1016/0003-4843(76)90018-8
T. G. McLaughlin, Gerald E. Sacks, Degrees of Unsolvability. The American Mathematical Monthly. ,vol. 72, pp. 804- ,(1965) , 10.2307/2314466
Paul Erdös, Richard Rado, A Combinatorial Theorem Journal of the London Mathematical Society. ,vol. s1-25, pp. 249- 255 ,(1950) , 10.1112/JLMS/S1-25.4.249