In mathematics, specifically set theory, an ordinal is said to be recursive if there is a recursive well-ordering of a subset of the natural numbers… (More)

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2007

2007

- Gerald E. Sacks
- 2007

Here we describe some results which will be proved in detail in [13] and [l4]. The notion of metarecursive set was introduced in… (More)

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2003

2003

- Hitoshi Kitada
- 2003

A question is proposed if a nonrecursive ordinal, the so-called Church-Kleene ordinal ω 1 really exists. We consider the systems… (More)

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2003

2003

Ordinals form the basis for termination proofs in ACL2. Currently, ACL2 uses a rather inefficient representation for the ordinals… (More)

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2000

2000

- Christian Choffrut, Serge Grigorieff
- Words, Languages & Combinatorics
- 2000

In order to explain the purpose of this paper, we recall briefly how the theory of “rationality” developed in the last fourty… (More)

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1996

1996

- Paul Taylor
- J. Symb. Log.
- 1996

Transitive extensional well founded relations provide an intuitionistic notion of ordinals which admits transfinite induction… (More)

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1994

1994

- John J. Thurber
- Arch. Math. Log.
- 1994

In this paper we will show how work of Ash and Love can be used to recover and strengthen the main results of Feiner in [F… (More)

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1993

1993

- Michael Rathjen
- Math. Log. Q.
- 1993

In ordinal analysis of impredicative theories so-called collapsing functions are of central importance. Unfortunately, the… (More)

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Highly Cited

1986

Highly Cited

1986

- Krzysztof R. Apt, Gordon D. Plotkin
- J. ACM
- 1986

Four semantics for a small programming language involving unbounded (but countable) nondeterminism are provided. These comprise… (More)

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1973

1973

- Leonard J. Bass, Paul Young
- J. ACM
- 1973

The relationship between computational complexity and hierarchies of computable Functions is explored. I t is shown that known… (More)

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1972