Some notes on plump ordinals
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918315867242496 |
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| author | Wang, Shuwei |
| author_facet | Wang, Shuwei |
| contents | In this exposition, we attempt to formalise a treatment of Paul Taylor's notion of plump ordinals in weak intuitionistic axiomatic set theories such as IKP. We will explore basic properties of plump ordinals, especially in relation to Gödel's constructible universe $L$ and incomparable codings. As a quick application, we explain at the end how plump ordinals can be used to build a Heyting-valued model $V^\mathbb{H}$ from a classical $V \vDash \mathrm{ZFC}$ such that for some arbitrary, fixed $x \in V$ we have $V^\mathbb{H} \vDash \mathcal{P}{\left(\check{x}\right)} \in L$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23070 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some notes on plump ordinals Wang, Shuwei Logic Primary: 03E70, Secondary: 03E10, 03F55 In this exposition, we attempt to formalise a treatment of Paul Taylor's notion of plump ordinals in weak intuitionistic axiomatic set theories such as IKP. We will explore basic properties of plump ordinals, especially in relation to Gödel's constructible universe $L$ and incomparable codings. As a quick application, we explain at the end how plump ordinals can be used to build a Heyting-valued model $V^\mathbb{H}$ from a classical $V \vDash \mathrm{ZFC}$ such that for some arbitrary, fixed $x \in V$ we have $V^\mathbb{H} \vDash \mathcal{P}{\left(\check{x}\right)} \in L$. |
| title | Some notes on plump ordinals |
| topic | Logic Primary: 03E70, Secondary: 03E10, 03F55 |
| url | https://arxiv.org/abs/2601.23070 |