A Note on Reducible Induction Schemata
✍ Scribed by H. E. Rose
- Publisher
- John Wiley and Sons
- Year
- 1965
- Tongue
- English
- Weight
- 229 KB
- Volume
- 11
- Category
- Article
- ISSN
- 0044-3050
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📜 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 Zermelo‐Fraenkel Set Theory, CZF. It is shown that CZF augmented by decidable Bar Induction proves the 1‐consistency of CZF. This answ
## MSC (2010) 03F30, 03H15 We characterize the sets of all Π2 and all B(Σ1 ) (= Boolean combinations of Σ1 ) theorems of IΠ - 1 in terms of restricted exponentiation, and use these characterizations to prove that both sets are not deductively equivalent. We also discuss how these results generaliz