Hanf numbers via accessible images
We present several new model-theoretic applications of the fact that, under the assumption that there exists a proper class of almost strongly compact cardinals, the powerful image of any accessible functor is accessible. In particular, we generalize to the context of accessible categories the recen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Logical Methods in Computer Science e.V.
2017-06-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/2190/pdf |
| _version_ | 1798018256586407936 |
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| author | Michael Lieberman Jiri Rosicky |
| author_facet | Michael Lieberman Jiri Rosicky |
| author_sort | Michael Lieberman |
| collection | DOAJ |
| description | We present several new model-theoretic applications of the fact that, under
the assumption that there exists a proper class of almost strongly compact
cardinals, the powerful image of any accessible functor is accessible. In
particular, we generalize to the context of accessible categories the recent
Hanf number computations of Baldwin and Boney, namely that in an abstract
elementary class (AEC) if the joint embedding and amalgamation properties hold
for models of size up to a sufficiently large cardinal, then they hold for
models of arbitrary size. Moreover, we prove that, under the above-mentioned
large cardinal assumption, every metric AEC is strongly d-tame, strengthening a
result of Boney and Zambrano and pointing the way to further generalizations. |
| first_indexed | 2024-04-11T16:20:54Z |
| format | Article |
| id | doaj.art-57cd71e664d64845aa526e0b5fca33ff |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-11T16:20:54Z |
| publishDate | 2017-06-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-57cd71e664d64845aa526e0b5fca33ff2022-12-22T04:14:22ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742017-06-01Volume 13, Issue 210.23638/LMCS-13(2:11)20172190Hanf numbers via accessible imagesMichael LiebermanJiri RosickyWe present several new model-theoretic applications of the fact that, under the assumption that there exists a proper class of almost strongly compact cardinals, the powerful image of any accessible functor is accessible. In particular, we generalize to the context of accessible categories the recent Hanf number computations of Baldwin and Boney, namely that in an abstract elementary class (AEC) if the joint embedding and amalgamation properties hold for models of size up to a sufficiently large cardinal, then they hold for models of arbitrary size. Moreover, we prove that, under the above-mentioned large cardinal assumption, every metric AEC is strongly d-tame, strengthening a result of Boney and Zambrano and pointing the way to further generalizations.https://lmcs.episciences.org/2190/pdfmathematics - logicmathematics - category theory03c95, 03c52, 18c35, 03e55 |
| spellingShingle | Michael Lieberman Jiri Rosicky Hanf numbers via accessible images Logical Methods in Computer Science mathematics - logic mathematics - category theory 03c95, 03c52, 18c35, 03e55 |
| title | Hanf numbers via accessible images |
| title_full | Hanf numbers via accessible images |
| title_fullStr | Hanf numbers via accessible images |
| title_full_unstemmed | Hanf numbers via accessible images |
| title_short | Hanf numbers via accessible images |
| title_sort | hanf numbers via accessible images |
| topic | mathematics - logic mathematics - category theory 03c95, 03c52, 18c35, 03e55 |
| url | https://lmcs.episciences.org/2190/pdf |
| work_keys_str_mv | AT michaellieberman hanfnumbersviaaccessibleimages AT jirirosicky hanfnumbersviaaccessibleimages |