Name
Abstract | ||
|---|---|---|
We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies (of various complexity) have been extensively studied, we point out that (if parameters are allowed) well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting $${(\Pi_1^0-\mathsf{CA}_0)_\alpha \vdash \mathsf{wf}(\alpha)\, {\rm where}\, (\Pi_1^0-\mathsf{CA}_0)_\alpha}$$ ( 1 0 - CA 0 ) wf ( ) where ( 1 0 - CA 0 ) stands for the iteration of $${\Pi^0_1}$$ 1 0 comprehension (with parameters) along some ordinal $${\alpha}$$ and $${\mathsf{wf}(\alpha)}$$ wf ( ) stands for the well-foundedness of $${\alpha}$$ . |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/s00153-014-0392-9 | Archive for Mathematical Logic |
Keywords | DocType | Volume |
pseudohierarchy,transfinite recursion,well-foundedness,03b30,second order set theory,03e70,03d75,03f35,intuitionistic logic,second order arithmetic | Journal | 53 |
Issue | ISSN | Citations |
7-8 | 1432-0665 | 1 |
PageRank | References | Authors |
0.39 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Dandolo Flumini | 1 | 1 | 0.39 |
| Kentaro Sato | 2 | 4 | 2.17 |