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- Helmut Schwichtenberg, Stanley S. Wainer
- Perspectives in logic
- 2012

- E. A. Cichon, Stanley S. Wainer
- J. Symb. Log.
- 1983

- Stanley S. Wainer
- J. Symb. Log.
- 1972

- Douglas A. Cenzer, Peter Clote, Rick L. Smith, Robert I. Soare, Stanley S. Wainer
- Ann. Pure Appl. Logic
- 1986

- Stanley S. Wainer
- J. Symb. Log.
- 1989

In this paper we use methods of proof theory to assign ordinals to classes of (terminating) programs, the idea being that the ordinal assignment provides a uniform way of measuring computational complexity \in the large". We are not concerned with placing prior (e.g. polynomial) bounds on computation{length, but rather with general methods of assessing the… (More)

- Geoffrey E. Ostrin, Stanley S. Wainer
- Ann. Pure Appl. Logic
- 2005

There is a quite natural way in which the safe/normal variable discipline of Bellantoni-Cook recursion (1992) can be imposed on arithmetical theories like PA: quantify over safes and induct on normals. This weakens the theory severely, so that the provably recursive functions become more realistically computable (slow growing rather than fast growing).… (More)

- Stanley S. Wainer
- Bulletin of Symbolic Logic
- 1999

The class of all recursive functions fails to possess a natural hierarchical structure, generated predicatively from “within”. On the other hand, many (proof-theoretically significant) sub-recursive classes do. This paper attempts to measure the limit of predicative generation in this context, by classifying and characterizing those (predictably… (More)

- Stanley S. Wainer
- J. Symb. Log.
- 1974

- Wilfried Sieg, Stanley S. Wainer
- CSL
- 1993

A "linear style" sequent calculus makes it possible to explore the close structural relationships between primitive recursive programs and their inductive termination proofs, and between program transformations and their corresponding proof transformations. In this context the recursive to tail recursive transformation corresponds proof theoretically to a… (More)