On products of ultrafilters
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912420952276992 |
|---|---|
| author | Goldberg, Gabriel |
| author_facet | Goldberg, Gabriel |
| contents | Assuming the Generalized Continuum Hypothesis, this paper answers the question: when is the tensor product of two ultrafilters equal to their Cartesian product? It is necessary and sufficient that their Cartesian product is an ultrafilter; that the two ultrafilters commute in the tensor product; that for all cardinals $λ$, one of the ultrafilters is both $λ$-indecomposable and $λ^+$-indecomposable; that the ultrapower embedding associated to each ultrafilter restricts to a definable embedding of the ultrapower of the universe associated to the other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_04677 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On products of ultrafilters Goldberg, Gabriel Logic Assuming the Generalized Continuum Hypothesis, this paper answers the question: when is the tensor product of two ultrafilters equal to their Cartesian product? It is necessary and sufficient that their Cartesian product is an ultrafilter; that the two ultrafilters commute in the tensor product; that for all cardinals $λ$, one of the ultrafilters is both $λ$-indecomposable and $λ^+$-indecomposable; that the ultrapower embedding associated to each ultrafilter restricts to a definable embedding of the ultrapower of the universe associated to the other. |
| title | On products of ultrafilters |
| topic | Logic |
| url | https://arxiv.org/abs/2102.04677 |