dc.contributor.author | Mesyan, Zak | |
dc.contributor.author | Mitchell, James D. | |
dc.contributor.author | Morayne, Michal | |
dc.contributor.author | Peresse, Yann | |
dc.date.accessioned | 2017-04-25T16:22:17Z | |
dc.date.available | 2017-04-25T16:22:17Z | |
dc.date.issued | 2012-11-01 | |
dc.identifier.citation | Mesyan , Z , Mitchell , J D , Morayne , M & Peresse , Y 2012 , ' The Bergman-Shelah Preorder on Transformation Semigroups ' , Mathematical Logic Quarterly , vol. 58 , no. 6 , pp. 424-433 . https://doi.org/10.1002/malq.201200002 | |
dc.identifier.issn | 0942-5616 | |
dc.identifier.uri | http://hdl.handle.net/2299/18077 | |
dc.description | This is the peer-reviewed version of the following article: Mesyan, Z., Mitchell, J. D., Morayne, M. and Péresse, Y. H. (2012), Mathematical Logic Quarterly, Vol. 58: 424–433, 'The Bergman-Shelah preorder on transformation semigroups', which has been published in final form at doi:10.1002/malq.201200002. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Copyright © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. http://www.interscience.wiley.com/ | |
dc.description.abstract | Let $\nat^\nat$ be the semigroup of all mappings on the natural numbers $\nat$, and let $U$ and $V$ be subsets of $\nat^\nat$. We write $U\preccurlyeq V$ if there exists a countable subset $C$ of $\nat^\nat$ such that $U$ is contained in the subsemigroup generated by $V$ and $C$. We give several results about the structure of the preorder $\preccurlyeq$. In particular, we show that a certain statement about this preorder is equivalent to the Continuum Hypothesis. The preorder $\preccurlyeq$ is analogous to one introduced by Bergman and Shelah on subgroups of the symmetric group on $\nat$. The results in this paper suggest that the preorder on subsemigroups of $\nat^\nat$ is much more complicated than that on subgroups of the symmetric group. | en |
dc.format.extent | 10 | |
dc.format.extent | 457145 | |
dc.language.iso | eng | |
dc.relation.ispartof | Mathematical Logic Quarterly | |
dc.subject | SEMIGROUPS | |
dc.subject | Topological Algebra | |
dc.subject | Continuum Hypothesis | |
dc.title | The Bergman-Shelah Preorder on Transformation Semigroups | en |
dc.contributor.institution | Mathematics and Theoretical Physics | |
dc.contributor.institution | School of Physics, Engineering & Computer Science | |
dc.contributor.institution | Department of Physics, Astronomy and Mathematics | |
dc.description.status | Peer reviewed | |
dc.identifier.url | http://arxiv.org/pdf/1109.2706v3.pdf | |
rioxxterms.versionofrecord | 10.1002/malq.201200002 | |
rioxxterms.type | Journal Article/Review | |
herts.preservation.rarelyaccessed | true | |