| Autor: |
Higuchi, Kojiro, Lempp, Steffen, Raghavan, Diip, Stephan, Frank |
| Rok vydání: |
2019 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We show that the order dimension of the partial order of all finite subsets of $\kappa$ under set inclusion is ${\log}_{2}({\log}_{2}(\kappa))$ whenever $\kappa$ is an infinite cardinal. We also show that the order dimension of any locally countable partial ordering $(P, <)$ of size $\kappa^+$, for any $\kappa$ of uncountable cofinality, is at most $\kappa$. In particular, this implies that it is consistent with ZFC that the dimension of the Turing degrees under partial ordering can be strictly less than the continuum. |
| Databáze: |
arXiv |
| Externí odkaz: |
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