Weak and Strong Versions of Effective Transfinite Recursion
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916603616034816 |
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| author | Uftring, Patrick |
| author_facet | Uftring, Patrick |
| contents | Working in the context of reverse mathematics, we give a fine-grained characterization result on the strength of two possible definitions for Effective Transfinite Recursion used in literature. Moreover, we show that $Π^0_2$-induction along a well-order $X$ is equivalent to the statement that the exponentiation of any well-order to the power of $X$ is well-founded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_05611 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Weak and Strong Versions of Effective Transfinite Recursion Uftring, Patrick Logic 03B30, 03F15, 03F35 Working in the context of reverse mathematics, we give a fine-grained characterization result on the strength of two possible definitions for Effective Transfinite Recursion used in literature. Moreover, we show that $Π^0_2$-induction along a well-order $X$ is equivalent to the statement that the exponentiation of any well-order to the power of $X$ is well-founded. |
| title | Weak and Strong Versions of Effective Transfinite Recursion |
| topic | Logic 03B30, 03F15, 03F35 |
| url | https://arxiv.org/abs/2202.05611 |