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1Peter G. Hinman. Recursion-theoretic Hierarchies. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, Heidelberg, and New York, 1978, XII + 480 Pp.

Wayne Richter

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1983Journal of Symbolic Logic（1983）

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2Yiannis N. Moschovakis. Elementary Induction on Abstract Structures. Studies in Logic and the Foundations of Mathematics, Vol. 77. North-Holland Publishing Company, Amsterdam and London, and American Elsevier Publishing Company, Inc., New York, 1974, X + 218 Pp.

Wayne Richter

Yiannis N. Moschovakis. Elementary induction on abstract structures. Studies in logic and the foundations of mathematics, vol. 77. North-Holland Publishing Company, Amsterdam and London, and American Elsevier Publishing Company, Inc., New York, 1974, x + 218 pp. - Volume 44 Issue 1

1979Journal of Symbolic Logic（1979）引用：23

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3Thomas J. Grilliot. Omitting Types: Application to Recursion Theory. the Journal of Symbolic Logic, Vol. 37 (1972), Pp. 81–89.

Wayne Richter

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1975Journal of Symbolic Logic（1975）引用：1

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4The least ∑ 2 1 and ∏ 2 1 reflecting ordinals

Wayne Richter

1975引用：1

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5N. V. Belyakin. A Variation of Richter's Construction of Ordinals. English Translation of X L 517. Algebra and Logic (new York), Vol. 8 (1969), Pp. 86–96.

Wayne Richter

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1975Journal of Symbolic Logic（1975）

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6Review: N. V. Belyakin, A Variation of Richter's Construction of Ordinals

Wayne Richter

1975Journal of Symbolic Logic（1975）引用：23

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7Inductive Definitions and Reflecting Properties of Admissible Ordinals

Wayne Richter,Peter Aczel

1974Studies in Logic and the Foundations of Mathematics（1974）引用：65

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8Review: Hisao Tanaka, on Analytic Well-orderings

Wayne Richter

1973Journal of Symbolic Logic（1973）引用：23

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9Hisao Tanaka. on Analytic Well-Orderings. the Journal of Symbolic Logic, Vol. 35 (1970), Pp. 198–204.

Wayne Richter

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1973Journal of Symbolic Logic（1973）

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10J. R. Shoenfield. A Hierarchy Based on a Type Two Object. Transactions of the American Mathematical Society, Vol. 134 (1968), Pp. 103–108.

Wayne Richter

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1971Journal of Symbolic Logic（1971）

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11Recursively Mahlo Ordinals and Inductive Definitions

Wayne Richter

This chapter discusses the recursively Mahlo ordinals and inductive definitions. A characterization of the first recursively Mahlo ordinal and the first recursively hyper-Mahlo ordinalis provided. The large countable ordinals are obtained as the closure ordinals of inductive definitions. Inductive definitions play a central role in hierarchy theory. A classic example is the theory of recursive ordinals. The usual systems of notations for the recursive ordinals are inductively defined by very simple (arithmetic) operations. A version of the Candy theorem on the existence of selection operators is the basic tool. A typical system is defined by an inductive definition consisting of several cases, depending on whether the ordinal reached at a given stage was zero, a successor, notationally singular, and notationally regular.

1971Studies in Logic and the Foundations of Mathematics LOGIC COLLOQUIUM '69（1971）引用：29

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12T. G. McLaughlin. Some Remarks on Extensibility, Confluence of Paths, Branching Properties, and Index Sets, for Certain Recursively Enumerable Graphs. Illinois Journal of Mathematics, Vol. 11 (1967), Pp. 257–279.

Wayne Richter

T. G. McLaughlin. Some remarks on extensibility, confluence of paths, branching properties, and index sets, for certain recursively enumerable graphs. Illinois journal of mathematics, vol. 11 (1967), pp. 257–279. - Volume 34 Issue 3

1969Journal of Symbolic Logic（1969）

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13Review: T. G. McLaughlin, Some Remarks on Extensibility, Confluence of Paths, Branching Properties, and Index Sets, for Certain Recursively Enumerable Graphs

Wayne Richter

1969Journal of Symbolic Logic（1969）引用：22

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14Constructively Accessible Ordinal Numbers.

W RICHTER

In [11] the constructive ordinals were extended to constructive finite number classes by using systems of notations where mappings at limit ordinals are just partial recursive functions. It turned out that these systems are equivalent, both in terms of ordinals represented and the forms of the sets of notations, to extensions obtained by using mappings at limit ordinals which are partial recursive in (sets of notations for) previously defined number classes. In this article these results are extended to constructive transfinite number classes. We present a system (F, ||) which, in terms of our analogy with the classical ordinals, provides notations for the ordinals less than the first “constructively inaccessible” ordinal, and show that the above equivalence holds at least this far.

1968Journal of Symbolic Logic（1968）引用：9

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15Review: Gaisi Takeuti, Akiko Kino, on Hierarchies of Predicates of Ordinal Numbers

Wayne Richter

1968Journal of Symbolic Logic（1968）引用：23

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16Review: Akiko Kino, A Note on Constructive Ordinals

Wayne Richter

1968Journal of Symbolic Logic（1968）引用：23

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17Gaisi Takeuti and Akiko Kino. on Hierarchies of Predicates of Ordinal Numbers. Journal of the Mathematical Society of Japan, Vol. 14 (1962), Pp. 199–232. - Akiko Kino and Gaisi Takeuti. A Note on Predicates of Ordinal Numbers. Journal of the Mathematical Society of Japan, Vol. 14 (1962), Pp. 367–378.

Wayne Richter

Gaisi Takeuti and Akiko Kino. On hierarchies of predicates of ordinal numbers. Journal of the Mathematical Society of Japan, vol. 14 (1962), pp. 199–232. - Akiko Kino and Gaisi Takeuti. A note on predicates of ordinal numbers. Journal of the Mathematical Society of Japan, vol. 14 (1962), pp. 367–378. - Volume 33 Issue 2

1968Journal of Symbolic Logic（1968）

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18Constructive Transfinite Number Classes

W RICHTER

1967BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY（1967）引用：19

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19Hilary Putnam. Uniqueness Ordinals in Higher Constructive Number Classes. Essays on the Foundations of Mathematics, Dedicated to A. A. Fraenkel on His Seventieth Anniversary, Edited by Y. Bar-Hillel, E. I. J. Poznanski, M. O. Rabin, and A. Robinson for the Hebrew University of Jerusalem, Magnes Press, Jerusalem 1961, and North-Holland Publishing Company, Amsterdam1962, Pp. 190–206.

Wayne Richter

Hilary Putnam. Uniqueness ordinals in higher constructive number classes. Essays on the foundations of mathematics, dedicated to A. A. Fraenkel on his seventieth anniversary, edited by Y. Bar-Hillel, E. I. J. Poznanski, M. O. Rabin, and A. Robinson for The Hebrew University of Jerusalem, Magnes Press, Jerusalem 1961, and North-Holland Publishing Company, Amsterdam1962, pp. 190–206. - Volume 31 Issue 1

1966Journal of Symbolic Logic（1966）

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20Hilary Putnam. on Hierarchies and Systems of Notations. Proceedings of the American Mathematical Society, Vol. 15 (1964), Pp. 44–50.

Wayne Richter

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1966Journal of Symbolic Logic（1966）

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Peter Aczel合作论文数University of Manchester, Manchester, Great Britain1

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