| Autor: |
Freund, Anton, Marcone, Alberto, Pakhomov, Fedor, Soldà, Giovanni |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
It has recently been shown that fairly strong axiom systems such as $\mathsf{ACA}_0$ cannot prove that the antichain with three elements is a better quasi order ($\mathsf{bqo}$). In the present paper, we give a complete characterization of the finite partial orders that are provably $\mathsf{bqo}$ in such axiom systems. The result will also be extended to infinite orders. As an application, we derive that a version of the minimal bad array lemma is weak over $\mathsf{ACA_0}$. In sharp contrast, a recent result shows that the same version is equivalent to $\Pi^1_2$-comprehension over the stronger base theory $\mathsf{ATR}_0$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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