## Bulletin of the American Mathematical Society

### Inductively defined sets of reals

Douglas Cenzer

#### Article information

Source
Bull. Amer. Math. Soc., Volume 80, Number 3 (1974), 485-487.

Dates
First available in Project Euclid: 4 July 2007

https://projecteuclid.org/euclid.bams/1183535523

Mathematical Reviews number (MathSciNet)
MR0406782

Zentralblatt MATH identifier
0328.02028

Subjects
Primary: 02F29
Secondary: 02F27 02F35 02K30

#### Citation

Cenzer, Douglas. Inductively defined sets of reals. Bull. Amer. Math. Soc. 80 (1974), no. 3, 485--487. https://projecteuclid.org/euclid.bams/1183535523

#### References

• 1. A. Blass and D. Cenzer, Cores of $\Pi^1_1$ sets of reals (to appear).
• 2. D. Cenzer, Monotone inductive definitions over the continuum, Notices Amer. Math. Soc. 21 (1974), A-19.
• 3. D. Cenzer, Ordinal recursion and inductive definitions, J. Fenstad and P. Hinman (Ed.), Generalized Recursion Theory, Oslo, 1972, North-Holland, Amsterdam (to appear).
• 4. D. Cenzer, Ordinal recursion over the continuum (to appear).
• 5. D. Cenzer, Parametric inductive definitions and recursive operators over the continuum (to appear).
• 6. T. Grilliot, Hierarchies based on objects of finite type, J. Symbolic Logic 34 (1969), 177-182. MR 44 #75.
• 7. P. Hinman, Recursion-theoretic hierarchies (to appear).
• 8. P. Hinman and Y. Moschovakis, Computability over the continuum, Logic Colloquium '69, North-Holland, Amsterdam, 1971, pp. 77-105.
• 9. S. C. Kleene, Recursive functionals and quantifiers of finite types. II, Trans. Amer. Math. Soc. 108 (1963), 106-142. MR 27 #3521.
• 10. W. Richter, Recursively Mahlo ordinals and inductive definitions, Logic Colloquium '69 (Proc. Summer School and Colloq., Manchester, 1969), North-Holland, Amsterdam, 1971, pp. 273-288. MR 43 #7331.