505 Citations
On the Intuitionistic Background of Gentzen's 1935 and 1936 Consistency Proofs and Their Philosophical Aspects
- Philosophy
- 2018
Gentzen’s three consistency proofs for elementary number theory have a common aim that originates from Hilbert’s Program, namely, the aim to justify the application of classical reasoning to…
Decoding Gentzen's Notation
- Mathematics
- 2018
In this note we consider Gentzen's first ordinal notation, used in his first published proof of the consistency of Peano Arithmetic (1936). It is a decimal notation, quite different from our current…
Commentary and Illocutionary Expressions in Linear Calculi of Natural Deduction
- Computer Science
- 2017
A linear natural deduction calculus is presented that makes use of formal illocutionsary expressions in such a way that unique readability for derivations is guaranteed – thus showing that formalizing illocutionary expressions can eliminate the need for commentary.
Goodstein’s Theorem Revisited
- Mathematics
- 2015
Prompted by Gentzen’s 1936 consistency proof, Goodstein found a close fit between descending sequences of ordinals \(<\varepsilon _{0}\) and sequences of integers, now known as Goodstein sequences.…
L O ] 1 8 M ay 2 01 4 Goodstein ’ s theorem revisited
- Mathematics
- 2014
Inspired by Gentzen’s 1936 consistency proof, Goodstein found a close fit between descending sequences of ordinals < ε0 and sequences of integers, now known as Goodstein sequences. This article…
Proof Theory : From arithmetic to set theory
- Mathematics, Philosophy
- 2013
In his Inaugural Dissertation from 1935 (published as [41]), Gentzen introduced his sequent calculus and employed the technique of cut elimination. As this is a tool of utmost importance in proof…
A MATHEMATICAL COMMITMENT WITHOUT COMPUTATIONAL STRENGTH
- Computer ScienceThe Review of Symbolic Logic
- 2021
This work considers a proper extension of Peano arithmetic by a mathematically meaningful axiom scheme that consists of sentences that assert that each computably enumerable property of finite binary trees has a finite basis.
Systems of Logic Based on Ordinals
- Computer ScienceAlan Turing's Systems of Logic
- 2021
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.
Size-based termination of higher-order rewriting
- Computer ScienceJournal of Functional Programming
- 2018
A general and modular criterion for the termination of simply typed λ-calculus extended with function symbols defined by user-defined rewrite rules is provided.
References
SHOWING 1-7 OF 7 REFERENCES
Begründung des „tertium non datur” mittels der Hilbertschen Theorie der Widerspruchsfreiheit
- Mathematics
- 1925
Formale Beweise und die Entscheidbarkeit
- Mathematics
- 1926
----------------------------------------------------Nutzungsbedingungen DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung…
Über die neue Grundlagenkrise der Mathematik
- Mathematics
- 1921
DigiZeitschriften e.V. gewährt ein nicht exklusives, nicht übertragbares, persönliches und beschränktes Recht auf Nutzung dieses Dokuments. Dieses Dokument ist ausschließlich für den persönlichen,…
Zum Hilbertschen Aufbau der reellen Zahlen
- Mathematics
- 1928
Um den Beweis fiir die yon Cantor aufgestellte Vermutung zu e~bringen, dal~ sich die Menge der ree|len Zahlen, d. h. der zaMentheoretischen I~unktionen, mi~ Hilfe der Zahlen de~ zweiten Zahlklasse…
Die Vollständigkeit der Axiome des logischen Funktionenkalküls
- Mathematics
- 1930
Jakina da Whiteheadek eta Russellek logika eta matematika eraiki dutela ageriko zenbait proposizio axiomatzat hartuz, eta horietatik, zehatz azaldutako inferentzia printzipioetan oinarrituz, logikako…