## Abstract Constructive set theory started with Myhill's seminal 1975 article [8]. This paper will be concerned with axiomatizations of the natural numbers in constructive set theory discerned in [3], clarifying the deductive relationships between these axiomatizations and the strength of various
Quotient topologies in constructive set theory and type theory
β Scribed by Hajime Ishihara; Erik Palmgren
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 196 KB
- Volume
- 141
- Category
- Article
- ISSN
- 0168-0072
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Bar Induction occupies a central place in Brouwerian mathematics. This note is concerned with the strength of Bar Induction on the basis of Constructive ZermeloβFraenkel Set Theory, CZF. It is shown that CZF augmented by decidable Bar Induction proves the 1βconsistency of CZF. This answ
We study constructive set theories, which deal with (partial) operations applying both to sets and operations themselves. Our starting point is a fully explicit, finitely axiomatized system ESTE of constructive sets and operations, which was shown in [10] to be as strong as PA. In this paper we cons