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Independence over arbitrary sets in NSOP1 theories |
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| Institution: | 1. School of Mathematics, University of Leeds, Leeds LS2 9JT, UK;2. Instytut Matematyczny Uniwersytetu Wroc?awskiego, pl. Grunwaldzki 2/4, 50-383 Wroc?aw, Poland;3. Department of Mathematics, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Republic of Korea;4. Department of Mathematics, UCLA, 520 Portola Plaza, Box 951555, Los Angeles, CA 90095, USA |
| Abstract: | We study Kim-independence over arbitrary sets. Assuming that forking satisfies existence, we establish Kim's lemma for Kim-dividing over arbitrary sets in an NSOP1 theory. We deduce symmetry of Kim-independence and the independence theorem for Lascar strong types. |
| Keywords: | Kim-dividing Extension Symmetry The independence theorem |
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