# 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…

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