Notions of weak genericity
- 1 September 1983
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 48 (3) , 764-770
- https://doi.org/10.2307/2273469
Abstract
This paper deals with forcing in arithmetic (as first introduced by Feferman [2]) and its connections with recursive function theory. We define for each n ≥ 1 the class of weakly n-generic sets. We prove that these classes merge with the classes of n-generic sets to form the hierarchy suggested by the terminology. Our notation is the same as that of Jockusch [5].Keywords
This publication has 6 references indexed in Scilit:
- Applications of Forcing to the Degree-Theory of the Arithmetical HierarchyProceedings of the London Mathematical Society, 1972
- Some applications of forcing to hierarchy problems in arithmeticMathematical Logic Quarterly, 1969
- The degrees of bi‐immune setsMathematical Logic Quarterly, 1969
- The Degrees of Hyperimmune SetsMathematical Logic Quarterly, 1968
- Some applications of the notions of forcing and generic setsFundamenta Mathematicae, 1964
- Retraceable SetsCanadian Journal of Mathematics, 1958