Transitivity of Kim-independence
| Autor: | Nicholas Ramsey, Itay Kaplan |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Transitive relation
General Mathematics 010102 general mathematics Mathematics - Logic Base (topology) 01 natural sciences Character (mathematics) 0103 physical sciences FOS: Mathematics Independence (mathematical logic) 010307 mathematical physics 0101 mathematics Logic (math.LO) Mathematical economics Mathematics |
| Popis: | We prove several results on the behavior of Kim-independence upon changing the base in NSOP$_{1}$ theories. As a consequence, we prove that Kim-independence satisfies transitivity and that this characterizes NSOP$_{1}$. Moreover, we characterize witnesses to Kim-dividing as exactly the $\ind^{K}$-Morley sequences. We give several applications, answering a number of open questions concerning transitivity, Morley sequences, and local character in NSOP$_{1}$ theories. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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