{"title":"有限情况下的后继不变性","authors":"Benjamin Rossman","doi":"10.1109/LICS.2003.1210054","DOIUrl":null,"url":null,"abstract":"A first-order sentence /spl theta/ of vocabulary /spl sigma/ /spl cup/ {S} is successor-invariant in the finite if for every finite /spl sigma/-structure M and successor relations S/sub 1/ and S/sub 2/ on M, (M, S/sub 1/) /spl vDash/ /spl theta/ /spl hArr/ (M, S/sub 2/) /spl vDash/ /spl theta/. In this paper I give an example of a non-first-order definable class of finite structures, which is, however, defined by a successor-invariant first-order sentence. This strengthens a corresponding result for order-invariant in the finite, due to Y. Gurevich.","PeriodicalId":280809,"journal":{"name":"18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.","volume":"41 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2003-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Successor-invariance in the finite\",\"authors\":\"Benjamin Rossman\",\"doi\":\"10.1109/LICS.2003.1210054\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A first-order sentence /spl theta/ of vocabulary /spl sigma/ /spl cup/ {S} is successor-invariant in the finite if for every finite /spl sigma/-structure M and successor relations S/sub 1/ and S/sub 2/ on M, (M, S/sub 1/) /spl vDash/ /spl theta/ /spl hArr/ (M, S/sub 2/) /spl vDash/ /spl theta/. In this paper I give an example of a non-first-order definable class of finite structures, which is, however, defined by a successor-invariant first-order sentence. This strengthens a corresponding result for order-invariant in the finite, due to Y. Gurevich.\",\"PeriodicalId\":280809,\"journal\":{\"name\":\"18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.\",\"volume\":\"41 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2003-06-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/LICS.2003.1210054\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"18th Annual IEEE Symposium of Logic in Computer Science, 2003. Proceedings.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS.2003.1210054","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A first-order sentence /spl theta/ of vocabulary /spl sigma/ /spl cup/ {S} is successor-invariant in the finite if for every finite /spl sigma/-structure M and successor relations S/sub 1/ and S/sub 2/ on M, (M, S/sub 1/) /spl vDash/ /spl theta/ /spl hArr/ (M, S/sub 2/) /spl vDash/ /spl theta/. In this paper I give an example of a non-first-order definable class of finite structures, which is, however, defined by a successor-invariant first-order sentence. This strengthens a corresponding result for order-invariant in the finite, due to Y. Gurevich.
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