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} }
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.
7 Citations
Unordered pairs in the set theory of Bourbaki 1949
- Mathematics
- 2010
Working informally in ZF, we build a pair of supertransitive models of Z, of which pair the union is shown to be a supertransitive model of Bourbaki’s 1949 system for set theory in which some…
INCOMPLETENESS VIA PARADOX AND COMPLETENESS
- PhilosophyThe Review of Symbolic Logic
- 2020
A generalization of the Arithmetized Completeness Theorem is presented whereby Russell’s paradox, a variant of Mirimanoff's paradox, the Liar, and the Grelling–Nelson paradox may be uniformly transformed into incompleteness theorems.
Transfinite recursion and computation in the iterative conception of set
- PhilosophySynthese
- 2014
This paper considers several kinds of recursion principles and proves results concerning their relation to one another, and considers philosophical motivations for these formal principles coming from the idea that computational notions lie at the core of the conception of set.
Mathematical Limits and Philosophical Significance of Transfinite Computation
- Mathematics
- 2014
Author(s): Rin, Benjamin | Advisor(s): Barrett, Jeffrey A; Walsh, Sean | Abstract: The general aim of this thesis is to explore applications of transfinite computation within the philosophy of…
Tight limits and completions from Dedekind-MacNeille to Lambek-Isbell
- MathematicsArXiv
- 2022
It is an open problem whether there exists a sup- and inf-complete category A ′′′′ with a sup- and inf-dense embedding A −→ A ′′′′ in analogy to the Dedekind completion of an ordered set. No Lambek…
References
SHOWING 1-10 OF 111 REFERENCES
Cantorian set theory and limitation of size
- Philosophy
- 1984
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
- Art
- 1996
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
- EconomicsJ. Symb. Log.
- 1943
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
- EconomicsJ. Symb. Log.
- 1942
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
- Mathematics, EconomicsJ. Symb. Log.
- 1937
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
- 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
- MathematicsJ. Symb. Log.
- 1942
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.