# Zur Hilbertschen Beweistheorie

@article{NeumannZurHB,
title={Zur Hilbertschen Beweistheorie},
author={John von Neumann},
journal={Mathematische Zeitschrift},
volume={26},
pages={1-46}
}
VON NEUMANN’S CONSISTENCY PROOF
• L. Bellotti
• Computer Science, Mathematics
• The Review of Symbolic Logic
• 2016
Von Neumann’s proof is the first rigorous proof of the consistency of an axiomatization of the first-order theory of a successor function. Expand
The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program
• R. Zach
• Mathematics, Computer Science
• Synthese
• 2004
The paper traces the development of the simultaneous development of logic and mathematics'' through the ∈-notation and provides an analysis of Ackermann's consistency proofs for primitive recursive arithmetic and for the first comprehensive mathematical system, the latter using thesubstitution method. Expand
A propósito del formalismo de Johann von Neumann
In 1930, Johann von Neumann, together with Rudolf Carnap and Arend Heyting, participated in a conference held in Konigsberg, called “Second Seminar on the Epistemology of Exact Sciences”. The ideaExpand
The consistency of arithmetic from a point of view of constructive tableau method with strong negation, Part I: the system without complete induction
In this Part I, we shall prove the consistency of arithmetic without complete induction from a point of view of strong negation, using its embedding to the tableau system $\bf SN$ of constructiveExpand
We must know -- We shall know
In this article, I focus on the resiliency of the P=?NP problem. The main point to deal with is the change of the underlying logic from first to second-order logic. In this manner, after developingExpand
From Solvability to Formal Decidability: Revisiting Hilbert’s “Non-Ignorabimus”
The topic of this article is Hilbert’s axiom of solvability, that is, his conviction of the solvability of every mathematical problem by means of a finite number of operations. The question ofExpand
NOMINALISTIC ORDINALS, RECURSION ON HIGHER TYPES, AND FINITISM
A historical account of the idea of nominalistic ordinals in the context of the Hilbert Programme as well as Gentzen and Bernays’ finitary interpretation of transfinite induction are presented. Expand
The Epsilon Calculus with Equality and Herbrand Complexity
• Mathematics, Computer Science
• ArXiv
• 2019
The contribution of this paper is the upper and lower bounds analysis of the length of Herbrand disjunctions in extended first ePSilon theorem for epsilon calculus with equality and shows that the complexity analysis for Herbrand's theorem with equality is a straightforward consequence of the one for extended firstepsilon theorem without equality. Expand
Interpreting Gödel : historical and philosophical perspectives
elements” (Ibid. p.383). Interestingly, Gödel describes this theorem as a reaction of the nature of mathematics itself, which is “very recalcitrant in the face of the Zeitgeist” (Ibid. p.379). TheExpand
Kalmár's Argument Against the Plausibility of Church's Thesis
In his famous paper, An Unsolvable Problem of Elementary Number Theory, Alonzo Church (1936) identified the intuitive notion of effective calculability with the mathematically precise notion ofExpand