Constructing illoyal algebra-valued models of set theory
An algebra-valued model of set theory is called loyal to its algebra if the model and its algebra have the same propositional logic; it is called faithful if all elements of the algebra are truth values of a sentence of the language of set theory in the model. We observe that non-trivial automorphis...
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| Veröffentlicht in: | Algebra universalis 2021-08, Vol.82 (3), Article 46 |
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| container_title | Algebra universalis |
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| creator | Löwe, Benedikt Paßmann, Robert Tarafder, Sourav |
| description | An algebra-valued model of set theory is called
loyal to its algebra
if the model and its algebra have the same propositional logic; it is called
faithful
if all elements of the algebra are truth values of a sentence of the language of set theory in the model. We observe that non-trivial automorphisms of the algebra result in models that are not faithful and apply this to construct three classes of illoyal models: tail stretches, transposition twists, and maximal twists. |
| doi_str_mv | 10.1007/s00012-021-00735-4 |
| format | Article |
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loyal to its algebra
if the model and its algebra have the same propositional logic; it is called
faithful
if all elements of the algebra are truth values of a sentence of the language of set theory in the model. We observe that non-trivial automorphisms of the algebra result in models that are not faithful and apply this to construct three classes of illoyal models: tail stretches, transposition twists, and maximal twists.</description><identifier>ISSN: 0002-5240</identifier><identifier>EISSN: 1420-8911</identifier><identifier>DOI: 10.1007/s00012-021-00735-4</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algebra ; Automorphisms ; Mathematics ; Mathematics and Statistics ; Set theory</subject><ispartof>Algebra universalis, 2021-08, Vol.82 (3), Article 46</ispartof><rights>The Author(s) 2021</rights><rights>The Author(s) 2021. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c293t-7d6567f79641b91e5ad6f465964c83bd0e6145c9a8dce514315c68139775d26a3</citedby><cites>FETCH-LOGICAL-c293t-7d6567f79641b91e5ad6f465964c83bd0e6145c9a8dce514315c68139775d26a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00012-021-00735-4$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00012-021-00735-4$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Löwe, Benedikt</creatorcontrib><creatorcontrib>Paßmann, Robert</creatorcontrib><creatorcontrib>Tarafder, Sourav</creatorcontrib><title>Constructing illoyal algebra-valued models of set theory</title><title>Algebra universalis</title><addtitle>Algebra Univers</addtitle><description>An algebra-valued model of set theory is called
loyal to its algebra
if the model and its algebra have the same propositional logic; it is called
faithful
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loyal to its algebra
if the model and its algebra have the same propositional logic; it is called
faithful
if all elements of the algebra are truth values of a sentence of the language of set theory in the model. We observe that non-trivial automorphisms of the algebra result in models that are not faithful and apply this to construct three classes of illoyal models: tail stretches, transposition twists, and maximal twists.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00012-021-00735-4</doi><oa>free_for_read</oa></addata></record> |
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| ispartof | Algebra universalis, 2021-08, Vol.82 (3), Article 46 |
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| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Automorphisms Mathematics Mathematics and Statistics Set theory |
| title | Constructing illoyal algebra-valued models of set theory |
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