Bernays and Set Theory

@article{Kanamori2009BernaysAS,
  title={Bernays and Set Theory},
  author={Akihiro Kanamori},
  journal={The Bulletin of Symbolic Logic},
  year={2009},
  volume={15},
  pages={43 - 69}
}
  • A. Kanamori
  • Published 1 March 2009
  • Philosophy
  • The Bulletin of Symbolic Logic
Abstract We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higher-order reflection principles. 
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References

SHOWING 1-10 OF 111 REFERENCES
Cantorian set theory and limitation of size
Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on
Logical dilemmas - the life and work of Kurt Gödel
TLDR
Kurt Goedel's seminal achievements that changed the perception and foundations of mathematics are explained in the context of his life from the turn of the century Austria to the Institute for Advanced Study in Princeton.
A System of Axiomatic Set Theory: Part V. General Set Theory
TLDR
The task in the treatment of general set theory will be to give a survey for the purpose of characterizing the different stages and the principal theorems with respect to their axiomatic requirements from the point of view of the system of axioms.
A System of Axiomatic Set Theory: Part IV. General Set Theory
TLDR
The task in the treatment of general set theory will be to give a survey for the purpose of characterizing the different stages and the principal theorems with respect to their axiomatic requirements from the point of view of the system of axioms.
The Theory of Classes a Modification of Von Neumann's System
TLDR
The theory of classes presented in this paper is a simplification of that presented by J. von Neumann in his paper Die Axiomatisierung der Mengenlehre, and the principal modifications of his system are the following.
AXIOM SCHEMATA OF STRONG INFINITY IN AXIOMATIC SET THEORY
  • A. Levy
  • Mathematics, Philosophy
  • 1960
l Introduction. There are, in general, two main approaches to the introduction of strong infinity assertions to the Zermelo-Fraenkel set theory. The arithmetical approach starts with the regular
A System of Axiomatic Set Theory: Part III. Infinity and Enumerability. Analysis
TLDR
This chapter begins with the definitions of infinity and enumerability and with some consideration of these concepts on the basis of the axioms I—III, IV, V a, V b, which are sufficient for general set theory.
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