# Beweisbarkeit und Unbeweisbarkeit von Anfangsfällen der transfiniten Induktion in der reinen Zahlentheorie

@article{Gentzen1943BeweisbarkeitUU, title={Beweisbarkeit und Unbeweisbarkeit von Anfangsf{\"a}llen der transfiniten Induktion in der reinen Zahlentheorie}, author={Gerhard Gentzen}, journal={Mathematische Annalen}, year={1943}, volume={119}, pages={140-161} }

## 139 Citations

The middle ground-ancestral logic

- Mathematics, Computer ScienceSynthese
- 2015

This work investigates a logic which is intermediate between FOL and SOL, and seems to be a particularly attractive alternative to both: ancestral logic, and presents two natural Gentzen-style proof systems for ancestral logic that encompass all forms of reasoning for this logic that are used in practice.

Construction principle and transfinite induction up to ε 0

- Mathematics
- 1982

What we call here the "construction principle" is a principle on the ground of which some functional can be defined; the domain and the range of such a functional consist of some "computable"…

Well-Ordering Principles in Proof Theory and Reverse Mathematics

- Mathematics
- 2020

Several theorems about the equivalence of familiar theories of reverse mathematics with certain well-ordering principles have been proved by recursion-theoretic and combinatorial methods (Friedman,…

W-Interfaces, Business Intelligence, and Content Processing

- Computer Science2013 IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies (IAT)
- 2013

A new design prototype for intelligent content management with multi-tier designs for interfaces is briefed and the paradigms can be applied to databases and query processing applications to predictive analyitics.

1 On founding the theory of algorithms

- 2011

My topic is the problem of “founding” the theory of algorithms, part of the more general problem of “founding” computer science; whether it needs founding—which, I will argue, it does; what should…

A hierarchy of ramified theories below primitive recursive arithmetic

- Mathematics
- 2010

The arithmetical theory EA(I;O) developed by Cagman, Ostrin and Wainer ([18] and [48]) provides a formal setting for the variable separation of Bellantoni-Cook predicative
recursion [6]. As such,…

Ways of Proof Theory

- Mathematics
- 2010

We suggest a new basic framework for the Weyl-Feferman predicativist program by constructing a formal predicative set theory PZF which resembles ZF . The basic idea is that the predicatively…

Arithmetical transfinite induction and hierarchies of functions

- Mathematics
- 1992

We generalize to the case of arithmetical transfinite induction the following three theorems for PA: the Wainer Theorem, the Paris–Harrington Theorem, and a version of the Solovay–Ketonen Theorem. We…

Sharpened lower bounds for cut elimination

- Computer Science, MathematicsThe Journal of Symbolic Logic
- 2012

These results remove the constant of proportionality, giving an exponential stack of height equal to d − O(1), which is based on more efficiently expressing the Gentzen–Solovay cut formulas as low depth formulas.

## References

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