Abstract
We modify the definable ultrapower construction of Kanovei and Shelah (2004) to develop a ZF-definable extension of the continuum with transfer provable using countable choice only, with an additional mild hypothesis on well-ordering implying properness. Under the same assumptions, we also prove the existence of a definable, proper elementary extension of the standard superstructure over the reals.
| Original language | English |
|---|---|
| Pages (from-to) | 385-391 |
| Number of pages | 7 |
| Journal | Journal of Symbolic Logic |
| Volume | 83 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Mar 2018 |
Bibliographical note
Publisher Copyright:© 2018 The Association for Symbolic Logic.
Funding
The authors are grateful to the anonymous JSL referee whose remarks and suggestions helped improve the article. Partial support of ESI at Vienna, during the visit of Vladimir Kanovei in December 2016 is acknowledged. Partial support of grant RFBR 17-01-00705 is acknowledged. This article is supported in part by Israel Science Foundation grant 1517/12. Partial support of grant RSF 14-50-00150 is acknowledged.
| Funders | Funder number |
|---|---|
| Israel Science Foundation | 1517/12 |
| Russian Science Foundation | 14-50-00150 |
Keywords
- definability
- hyperreal
- superstructure