We investigate the configuration where a group of finite Morley rank acts definably and generically m -transitively on an elementary abelian p -group of Morley rank n , where p is an odd prime, and m ⩾ n . We conclude that m = n , and the action is equivalent to the natural action of GL n ( F ) on F n for some algebraically closed field F . This strengthens one of our earlier results, and partially answers two problems posed by Borovik and Cherlin in 2008.
我们研究了这样的配置，其中有限Morley秩的组可定义地和一般地m -传递作用于Morley秩n的初等阿贝儿p -群，其中p是奇数素数，并且m大于或等于n。我们得出m = n的结论，并且对于某些代数闭场F，其作用等价于GL n (F)对F n的自然作用。这加强了我们早期的一个结果，并部分回答了Borovik和Cherlin在2008年提出的两个问题。
{"title":"Groups of finite Morley rank with a generically multiply transitive action on an abelian group","authors":"A. Berkman, A. Borovik","doi":"10.2140/mt.2022.1.1","DOIUrl":"https://doi.org/10.2140/mt.2022.1.1","url":null,"abstract":"We investigate the configuration where a group of finite Morley rank acts definably and generically m -transitively on an elementary abelian p -group of Morley rank n , where p is an odd prime, and m ⩾ n . We conclude that m = n , and the action is equivalent to the natural action of GL n ( F ) on F n for some algebraically closed field F . This strengthens one of our earlier results, and partially answers two problems posed by Borovik and Cherlin in 2008.","PeriodicalId":21757,"journal":{"name":"Simul. Model. Pract. Theory","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87388048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Based on Hrushovski, Palac{'i}n and Pillay's example [6], we produce a new structure without the canonical base property, which is interpretable in Baudisch's group. Said structure is, in particular, CM-trivial, and thus at the lowest possible level of the ample hierarchy.
{"title":"CM-trivial structures without the canonical base property","authors":"Thomas Blossier, Léo Jimenez","doi":"10.2140/mt.2022.1.31","DOIUrl":"https://doi.org/10.2140/mt.2022.1.31","url":null,"abstract":"Based on Hrushovski, Palac{'i}n and Pillay's example [6], we produce a new structure without the canonical base property, which is interpretable in Baudisch's group. Said structure is, in particular, CM-trivial, and thus at the lowest possible level of the ample hierarchy.","PeriodicalId":21757,"journal":{"name":"Simul. Model. Pract. Theory","volume":"16 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87868149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
An important dividing line in the class of unstable theories is being NSOP$_1$, which is more general than being simple. In NSOP$_1$ theories forking independence may not be as well-behaved as in stable or simple theories, so it is replaced by another independence notion, called Kim-independence. We generalise Kim-independence over models in NSOP$_1$ theories to positive logic -- a proper generalisation of first-order logic where negation is not built in, but can be added as desired. For example, an important application is that we can add hyperimaginary sorts to a positive theory to get another positive theory, preserving NSOP$_1$ and various other properties. We prove that, in a thick positive NSOP$_1$ theory, Kim-independence over existentially closed models has all the nice properties that it is known to have in a first-order NSOP$_1$ theory. We also provide a Kim-Pillay style theorem, characterising which thick positive theories are NSOP$_1$ by the existence of a certain independence relation. Furthermore, this independence relation must then be the same as Kim-independence. Thickness is the mild assumption that being an indiscernible sequence is type-definable. In first-order logic Kim-independence is defined in terms of Morley sequences in global invariant types. These may not exist in thick positive theories. We solve this by working with Morley sequences in global Lascar-invariant types, which do exist in thick positive theories. We also simplify certain tree constructions that were used in the study of Kim-independence in first-order theories. In particular, we only work with trees of finite height.
{"title":"Kim-independence in positive logic","authors":"J. Dobrowolski, M. Kamsma","doi":"10.2140/mt.2022.1.55","DOIUrl":"https://doi.org/10.2140/mt.2022.1.55","url":null,"abstract":"An important dividing line in the class of unstable theories is being NSOP$_1$, which is more general than being simple. In NSOP$_1$ theories forking independence may not be as well-behaved as in stable or simple theories, so it is replaced by another independence notion, called Kim-independence. We generalise Kim-independence over models in NSOP$_1$ theories to positive logic -- a proper generalisation of first-order logic where negation is not built in, but can be added as desired. For example, an important application is that we can add hyperimaginary sorts to a positive theory to get another positive theory, preserving NSOP$_1$ and various other properties. We prove that, in a thick positive NSOP$_1$ theory, Kim-independence over existentially closed models has all the nice properties that it is known to have in a first-order NSOP$_1$ theory. We also provide a Kim-Pillay style theorem, characterising which thick positive theories are NSOP$_1$ by the existence of a certain independence relation. Furthermore, this independence relation must then be the same as Kim-independence. Thickness is the mild assumption that being an indiscernible sequence is type-definable. In first-order logic Kim-independence is defined in terms of Morley sequences in global invariant types. These may not exist in thick positive theories. We solve this by working with Morley sequences in global Lascar-invariant types, which do exist in thick positive theories. We also simplify certain tree constructions that were used in the study of Kim-independence in first-order theories. In particular, we only work with trees of finite height.","PeriodicalId":21757,"journal":{"name":"Simul. Model. Pract. Theory","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87107783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate Keisler measures in arbitrary theories. Our initial focus is on Borel definability. We show that when working over countable parameter sets in countable theories, Borel definable measures are closed under Morley products and satisfy associativity. However, we also demonstrate failures of both properties over uncountable parameter sets. In particular, we show that the Morley product of Borel definable types need not be Borel definable (correcting an erroneous result from the literature). We then study various notions of generic stability for Keisler measures and generalize several results from the NIP setting to arbitrary theories. We also prove some positive results for the class of frequency interpretation measures in arbitrary theories, namely, that such measures are closed under convex combinations and commute with all Borel definable measures. Finally, we construct the first example of a complete type which is definable and finitely satisfiable in a small model, but not finitely approximated over any small model.
{"title":"Keisler measures in the wild","authors":"G. Conant, K. Gannon, James Hanson","doi":"10.2140/mt.2023.2.1","DOIUrl":"https://doi.org/10.2140/mt.2023.2.1","url":null,"abstract":"We investigate Keisler measures in arbitrary theories. Our initial focus is on Borel definability. We show that when working over countable parameter sets in countable theories, Borel definable measures are closed under Morley products and satisfy associativity. However, we also demonstrate failures of both properties over uncountable parameter sets. In particular, we show that the Morley product of Borel definable types need not be Borel definable (correcting an erroneous result from the literature). We then study various notions of generic stability for Keisler measures and generalize several results from the NIP setting to arbitrary theories. We also prove some positive results for the class of frequency interpretation measures in arbitrary theories, namely, that such measures are closed under convex combinations and commute with all Borel definable measures. Finally, we construct the first example of a complete type which is definable and finitely satisfiable in a small model, but not finitely approximated over any small model.","PeriodicalId":21757,"journal":{"name":"Simul. Model. Pract. Theory","volume":"303 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86765389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-01DOI: 10.1016/j.simpat.2020.102231
A. Schilling, Kaitlin Salscheider, H. Rusche, H. Jasak, M. Fehlbier, S. Kohlstädt
{"title":"Approach on simulation of solidification and shrinkage of gravity cast salt cores","authors":"A. Schilling, Kaitlin Salscheider, H. Rusche, H. Jasak, M. Fehlbier, S. Kohlstädt","doi":"10.1016/j.simpat.2020.102231","DOIUrl":"https://doi.org/10.1016/j.simpat.2020.102231","url":null,"abstract":"","PeriodicalId":21757,"journal":{"name":"Simul. Model. Pract. Theory","volume":"18 1","pages":"102231"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73685347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-01DOI: 10.1016/j.simpat.2020.102232
Yannis Spyridis, T. Lagkas, P. Sarigiannidis, Jie Zhang
{"title":"Modelling and simulation of a new cooperative algorithm for UAV swarm coordination in mobile RF target tracking","authors":"Yannis Spyridis, T. Lagkas, P. Sarigiannidis, Jie Zhang","doi":"10.1016/j.simpat.2020.102232","DOIUrl":"https://doi.org/10.1016/j.simpat.2020.102232","url":null,"abstract":"","PeriodicalId":21757,"journal":{"name":"Simul. Model. Pract. Theory","volume":"96 1","pages":"102232"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81049026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-01DOI: 10.1016/j.simpat.2020.102215
Zhiwei Guo, Yu Shen, M. Aloqaily, Y. Jararweh, Keping Yu
{"title":"Probabilistic inference-based modeling for sustainable environmental systems under hybrid cloud infrastructure","authors":"Zhiwei Guo, Yu Shen, M. Aloqaily, Y. Jararweh, Keping Yu","doi":"10.1016/j.simpat.2020.102215","DOIUrl":"https://doi.org/10.1016/j.simpat.2020.102215","url":null,"abstract":"","PeriodicalId":21757,"journal":{"name":"Simul. Model. Pract. Theory","volume":"295 1","pages":"102215"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89066646","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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