{"title":"魔杖/集合理论：实现康威的数学家解放运动，并应用于具有普遍集合的教会集合论","authors":"TIM BUTTON","doi":"10.1017/jsl.2024.21","DOIUrl":null,"url":null,"abstract":"<p>Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands).</p><p>By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive way of fleshing out this idea is synonymous with a ZF-like theory.</p><p>This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974).</p>","PeriodicalId":501300,"journal":{"name":"The Journal of Symbolic Logic","volume":"20 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"WAND/SET THEORIES: A REALIZATION OF CONWAY’S MATHEMATICIANS’ LIBERATION MOVEMENT, WITH AN APPLICATION TO CHURCH’S SET THEORY WITH A UNIVERSAL SET\",\"authors\":\"TIM BUTTON\",\"doi\":\"10.1017/jsl.2024.21\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands).</p><p>By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive way of fleshing out this idea is synonymous with a ZF-like theory.</p><p>This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974).</p>\",\"PeriodicalId\":501300,\"journal\":{\"name\":\"The Journal of Symbolic Logic\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Journal of Symbolic Logic\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/jsl.2024.21\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Symbolic Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/jsl.2024.21","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
WAND/SET THEORIES: A REALIZATION OF CONWAY’S MATHEMATICIANS’ LIBERATION MOVEMENT, WITH AN APPLICATION TO CHURCH’S SET THEORY WITH A UNIVERSAL SET
Consider a variant of the usual story about the iterative conception of sets. As usual, at every stage, you find all the (bland) sets of objects which you found earlier. But you also find the result of tapping any earlier-found object with any magic wand (from a given stock of magic wands).
By varying the number and behaviour of the wands, we can flesh out this idea in many different ways. This paper's main Theorem is that any loosely constructive way of fleshing out this idea is synonymous with a ZF-like theory.
This Theorem has rich applications; it realizes John Conway's (1976) Mathematicians' Liberation Movement; and it connects with a lovely idea due to Alonzo Church (1974).
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