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{"title":"Δ20$mathbf\\{Delta }^0_2$ Ω-幂的瓦奇度","authors":"Olivier Finkel, Dominique Lecomte","doi":"10.1002/malq.202400024","DOIUrl":null,"url":null,"abstract":"<p>We provide, for each natural number <span></span><math>\n <semantics>\n <mi>n</mi>\n <annotation>$n$</annotation>\n </semantics></math> and each class among <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>D</mi>\n <mi>n</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <msubsup>\n <mi>Σ</mi>\n <mn>1</mn>\n <mn>0</mn>\n </msubsup>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$D_n(\\mathbf {\\Sigma }^0_1)$</annotation>\n </semantics></math>, <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mover>\n <mi>D</mi>\n <mo>̌</mo>\n </mover>\n <mi>n</mi>\n </msub>\n <mrow>\n <mo>(</mo>\n <msubsup>\n <mi>Σ</mi>\n <mn>1</mn>\n <mn>0</mn>\n </msubsup>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\check{D}_n(\\mathbf {\\Sigma }^0_1)$</annotation>\n </semantics></math>, <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>D</mi>\n <mrow>\n <mn>2</mn>\n <mi>n</mi>\n <mo>+</mo>\n <mn>1</mn>\n </mrow>\n </msub>\n <mrow>\n <mo>(</mo>\n <msubsup>\n <mi>Σ</mi>\n <mn>1</mn>\n <mn>0</mn>\n </msubsup>\n <mo>)</mo>\n </mrow>\n <mi>⊕</mi>\n <msub>\n <mover>\n <mi>D</mi>\n <mo>̌</mo>\n </mover>\n <mrow>\n <mn>2</mn>\n <mi>n</mi>\n <mo>+</mo>\n <mn>1</mn>\n </mrow>\n </msub>\n <mrow>\n <mo>(</mo>\n <msubsup>\n <mi>Σ</mi>\n <mn>1</mn>\n <mn>0</mn>\n </msubsup>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$D_{2n+1}(\\mathbf {\\Sigma }^0_1)\\oplus \\check{D}_{2n+1}(\\mathbf {\\Sigma }^0_1)$</annotation>\n </semantics></math>, a regular language whose associated omega-power is complete for this class.</p>","PeriodicalId":49864,"journal":{"name":"Mathematical Logic Quarterly","volume":"70 3","pages":"286-293"},"PeriodicalIF":0.4000,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Wadge degrees of \\n \\n \\n Δ\\n 2\\n 0\\n \\n $\\\\mathbf{\\\\Delta }^0_2$\\n omega-powers\",\"authors\":\"Olivier Finkel, Dominique Lecomte\",\"doi\":\"10.1002/malq.202400024\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We provide, for each natural number <span></span><math>\\n <semantics>\\n <mi>n</mi>\\n <annotation>$n$</annotation>\\n </semantics></math> and each class among <span></span><math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mi>D</mi>\\n <mi>n</mi>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <msubsup>\\n <mi>Σ</mi>\\n <mn>1</mn>\\n <mn>0</mn>\\n </msubsup>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$D_n(\\\\mathbf {\\\\Sigma }^0_1)$</annotation>\\n </semantics></math>, <span></span><math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mover>\\n <mi>D</mi>\\n <mo>̌</mo>\\n </mover>\\n <mi>n</mi>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <msubsup>\\n <mi>Σ</mi>\\n <mn>1</mn>\\n <mn>0</mn>\\n </msubsup>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$\\\\check{D}_n(\\\\mathbf {\\\\Sigma }^0_1)$</annotation>\\n </semantics></math>, <span></span><math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mi>D</mi>\\n <mrow>\\n <mn>2</mn>\\n <mi>n</mi>\\n <mo>+</mo>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <msubsup>\\n <mi>Σ</mi>\\n <mn>1</mn>\\n <mn>0</mn>\\n </msubsup>\\n <mo>)</mo>\\n </mrow>\\n <mi>⊕</mi>\\n <msub>\\n <mover>\\n <mi>D</mi>\\n <mo>̌</mo>\\n </mover>\\n <mrow>\\n <mn>2</mn>\\n <mi>n</mi>\\n <mo>+</mo>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n <mrow>\\n <mo>(</mo>\\n <msubsup>\\n <mi>Σ</mi>\\n <mn>1</mn>\\n <mn>0</mn>\\n </msubsup>\\n <mo>)</mo>\\n </mrow>\\n </mrow>\\n <annotation>$D_{2n+1}(\\\\mathbf {\\\\Sigma }^0_1)\\\\oplus \\\\check{D}_{2n+1}(\\\\mathbf {\\\\Sigma }^0_1)$</annotation>\\n </semantics></math>, a regular language whose associated omega-power is complete for this class.</p>\",\"PeriodicalId\":49864,\"journal\":{\"name\":\"Mathematical Logic Quarterly\",\"volume\":\"70 3\",\"pages\":\"286-293\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-09-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Logic Quarterly\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/malq.202400024\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Logic Quarterly","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/malq.202400024","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
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