Probleme der Grundlegung der Mathematik

  title={Probleme der Grundlegung der Mathematik},
  author={David R. Hilbert},
  journal={Mathematische Annalen},
  • D. Hilbert
  • Published 1 December 1930
  • Mathematics
  • Mathematische Annalen
Hilbert's Program Revisited
After sketching the main lines of Hilbert's program, certain well-known andinfluential interpretations of the program are critically evaluated, and analternative interpretation is presented. Finally,
Kurt Gödel , ‘ Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme I ’ ( 1931 )
First publication: Monatshefte f ür Mathematik und Physik , 37, 173–198 Reprints:S. Feferman et al., eds., Kurt Gödel. Collected Works. Volume I: Publications 1929–1936. New York: Oxford University
The integral Chow ring of $\mathcal{M}_{0}(\mathbb{P}^r, d)$, for $d$ odd
For any odd integer d, we give a presentation for the integral Chow ring of the stack M0(P, d), as a quotient of the polynomial ring Z[c1, c2]. We describe an efficient set of generators for the
Lorenzen Between Gentzen and Schütte
We discuss Lorenzen’s consistency proof for ramified type theory without reducibility, published in 1951, in its historical context and highlight Lorenzen’s contribution to the development of modern
Formalism and Hilbert's understanding of consistency problems
This paper will highlight what it sees as the salient points of connection between Hilbert’s formalist attitude and his finitist standard for the consistency proof for arithmetic and his expressed hope that his solution of that problem would dispense with certain epistemological concerns regarding arithmetic once and for all.
Methodological Frames: Paul Bernays, Mathematical Structuralism, and Proof Theory
sphere; in this sphere, the structure of their connection presents itself as an object of pure mathematical thinking and is being investigated with the sole focus on logical relations.38 36 The three
Axioms and Formalisms
The Fregean work profoundly changed the authors' understanding of the relationship between logic and mathematics, of the possibilities of formal systems and of the role of infinity in mathematics, while at the same time opening the way to new disciplines such as proof theory and making it possible to build a foundation on which computer science could then be born and develop.
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 of
A Most Interesting, but Revoked Draft for Hilbert and Bernays' "Grundlagen der Mathematik" That Never Found Its Way into Publication, and a CV of Hasenjaeger
A third of a century later, Bernays' preface to the second edition (1968) of the first volume of Hilbert and Bernays' "Grundlagen der Mathematik" mentions joint work of Hasenjaeger and Bernays on the