Abstract
We study NSOP1 theories. We define Kim-independence, which generalizes non-forking independence in simple theories and corresponds to non-forking at a generic scale. We show that Kim-independence satisfies a version of Kim's lemma, local character, symmetry, and an independence theorem, and that moreover these properties individually characterize NSOP1 theories. We describe Kim-independence in several concrete theories and observe that it corresponds to previously studied notions of independence in Frobenius fields and vector spaces with a generic bilinear form.
| Original language | English |
|---|---|
| Pages (from-to) | 1423-1474 |
| Number of pages | 52 |
| Journal | Journal of the European Mathematical Society |
| Volume | 22 |
| Issue number | 5 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Funding Information:The first author would like to thank the Israel Science Foundation for partial support of this research (Grant no. 1533/14).
Publisher Copyright:
© European Mathematical Society 2020
Keywords
- Kim-independence
- NSOP
- Simple theories