|
JAIST Repository >
School of Information Science >
Articles >
Journal Articles >
Please use this identifier to cite or link to this item:
http://hdl.handle.net/10119/10866
|
| Title: | On the contrapositive of countable choice |
| Authors: | Ishihara, Hajime
Schuster, Peter |
| Keywords: | Contrapositive of countable choice
Double negation elimination
Heyting arithmetic
Elementary analysis |
| Issue Date: | 2010-09-18 |
| Publisher: | Springer |
| Magazine name: | Archive for Mathematical Logic |
| Volume: | 50 |
| Number: | 1-2 |
| Start page: | 137 |
| End page: | 143 |
| DOI: | 10.1007/s00153-010-0205-8 |
| Abstract: | We show that in elementary analysis (EL) the contrapositive of countable choice (CCC) is equivalent to double negation elimination for Σ^0_2-formulas. By also proving a recursive adaptation of this equivalence in Heyting arithmetic (HA), we give an instance of the conservativity of EL over HA with respect to recursive functions and predicates. As a complement, we prove in HA enriched with the (extended) Church thesis that every decidable predicate is recursive. |
| Rights: | This is the author-created version of Springer, Hajime Ishihara and Peter Schuster, Archive for Mathematical Logic, 50(1-2), 2010, 137-143. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/s00153-010-0205-8 |
| URI: | http://hdl.handle.net/10119/10866 |
| Material Type: | author |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
|
Files in This Item:
| File |
Description |
Size | Format |
|---|
| 15850.pdf | | 111Kb | Adobe PDF | View/Open |
|
All items in DSpace are protected by copyright, with all rights reserved.
|
