# 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} }

## 140 Citations

The middle ground-ancestral logic

- 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

- Computer Science
- 2011

The paper splits naturally into two parts: a general introduction in Sections 1 – 4 which lays out the problem and reviews briefly the various approaches to it in the literature, and a more specific outline of the proposed solution, beginning with Section 5.

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

- Computer Science
- 2010

A new basic framework for the Weyl-Feferman predicativist program is suggested by constructing a formal predicative set theory PZF which resembles ZF, and which reflects real mathematical practice in making an extensive use of statically defined abstract set terms.

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…

Representation and Reality by Language: How to Make a Home Quantum Computer?

- Computer ScienceSSRN Electronic Journal
- 2020

A set theory model of reality, representation and language based on the relation of completeness and incompleteness is explored and the equivalence of that model to a quantum computer is demonstrated.

## References

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