Über die Existenz unabhängiger Axiomensysteme zu unendlichen Satzsystemen

  title={{\"U}ber die Existenz unabh{\"a}ngiger Axiomensysteme zu unendlichen Satzsystemen},
  author={Gerhard Gentzen},
  journal={Mathematische Annalen},
  • G. Gentzen
  • Published 1 December 1933
  • Mathematics
  • Mathematische Annalen
Stoic Sequent Logic and Proof Theory
This paper contends that Stoic logic (i.e. Stoic analysis) deserves more attention from contemporary logicians. It sets out how, compared with contemporary propositional calculi, Stoic analysis is
A New Representation Theorem for Many-valued Modal Logics
  • Z. Majkic
  • Computer Science, Mathematics
  • 2011
We propose a new definition of the representation theorem for many-valued logics, with modal operators as well, and define the stronger relationship between algebraic models of a given logic and
Autoreferential semantics for many-valued modal logics
  • Z. Majkic
  • Mathematics, Computer Science
    J. Appl. Non Class. Logics
  • 2008
The autoreferential Kripke-style semantics for this class of modal algebras is based on the set of possible worlds equal to the complete lattice of algebraic truth-values, while all intermediate possible worlds represent the different levels of paraconsistent logics.
Resolution and the Origins of Structural Reasoning: Early Proof-Theoretic Ideas of Hertz and Gentzen
It is shown that Paul Hertz anticipated important techniques and results of general proof theory as well as of resolution theory, if the latter is regarded as a part of structural proof theory.
Semantic Values for Natural Deduction Derivations
Drawing upon Martin-Löf’s semantic framework for his constructive type theory, semantic values are assigned also to natural-deduction derivations, while observing the crucial distinction between
The Consistency of Arithmetic
  • R. Meyer
  • The Australasian Journal of Logic
  • 2021
This paper offers an elementary proof that formal arithmetic is consistent. The system that will be proved consistent is a first-order theory R♯, based as usual on the Peano postulates and the
The Deduction Theorem ( before and after Herbrand ) C
  • 2021
Attempts to articulate the real meaning or ultimate significance of a famous theorem comprise a major vein of philosophical writing about mathematics. The subfield of mathematical logic has supplied
Metalogic, Schopenhauer and Universal Logic
Schopenhauer used the word “metalogical” since his first work, On the Fourfold Root of the Principle of Sufficient Reason (1813), being the first to give it a precise meaning and a proper place
The Explosion Calculus
A calculus for classical propositional sequents is introduced that consists of a restricted version of the cut rule and local variants of the logical rules that explode a given sequent into its elementary structural sequents, which do not contain any logical constants.
Analyticity, Balance and Non-admissibility of $$\varvec{Cut}$$Cut in Stoic Logic
This paper shows that, for the Hertz–Gentzen Systems of 1933 (without Thinning), all derivations are analytic: every cut formula occurs as a subformula in the cut’s conclusion.