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- Anne Sjerp Troelstra, Helmut Schwichtenberg
- Cambridge tracts in theoretical computer science
- 1996

1. Introduction 2. N-systems and H-systems 3. Gentzen systems 4. Cut elimination with applications 5. Bounds and permutations 6. Normalization for natural deduction 7. Resolution 8. Categorical logic… (More)

- Ulrich Berger, Helmut Schwichtenberg
- LICS
- 1991

Publisher Summary This chapter discusses the Cut-Elimination Theorem for first-order logic. The proof of Cut-Elimination Theorem is set up in such a way that it can be easily generalized to many… (More)

- Helmut Schwichtenberg
- Arch. Math. Log.
- 1991

It is well known that the full reduction tree for any term of the typed 2-calculus is finite. However, it is not obvious how a reasonable estimate for its height might be obtained. Here we note that… (More)

- Stephen J. Bellantoni, Karl-Heinz Niggl, Helmut Schwichtenberg
- Ann. Pure Appl. Logic
- 2000

Abstract It is shown how to restrict recursion on notation in all finite types so as to characterize the polynomial-time computable functions. The restrictions are obtained by using a ramified type… (More)

- Helmut Schwichtenberg
- Theor. Comput. Sci.
- 1999

It is shown that permutative conversions terminate for the cut-free intuitionistic Gentzen (i.e. sequent) calculus; this proves a conjecture by Dyckhoff and Pinto. The main technical tool is a term… (More)

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

Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique… (More)