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Automorphism Groups of Substructure Lattices of Vector Spaces in Computable Algebra [chapter]

Rumen Dimitrov, Valentina Harizanov, Andrei Morozov
<span title="">2016</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Harizanov, "The lattice of computably enumerable vector spaces," in: Computability and Complexity, A. Day, M. Fellows, N.  ...  Harizanov, "Groups with orderings of arbitrary algorithmic complexity," 22 pages, accepted for publication in: Sets and Computations (IMS, National University of Singapore), R. Dilip, S.D.  ...  "Inductive inference of classes of computably enumerable vector spaces," Logic Seminar, Cornell University, December 2004. Dissertation Committees 15.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-40189-8_26">doi:10.1007/978-3-319-40189-8_26</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2p5s2kf5xzfwfdf7zakfx43mpy">fatcat:2p5s2kf5xzfwfdf7zakfx43mpy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170607040607/http://home.gwu.edu/~harizanv/vharizanovcv.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b7/85/b78528c883f24cbcf212205a9f11bbc2f14d2a88.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-40189-8_26"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Turing Degrees and Automorphism Groups of Substructure Lattices [article]

Rumen Dimitrov, Valentina Harizanov, Andrey Morozov
<span title="2018-11-03">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In particular, for a Turing degree d, we investigate the groups of d -computable automorphisms of the lattice of d-computably enumerable vector spaces, of the interval Boolean algebra B_η of the ordered  ...  In this paper, we focus on the lattice structure of computably enumerable substructures of a given canonical computable structure.  ...  By Theorem 12, we conclude that ∅ ′′ is computable in any copy of Aut 0 (B η ). Clearly, we can construct a specific copy of Aut 0 (B η ), which is computable in ∅ ′′ .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1811.01224v1">arXiv:1811.01224v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kzgwkxfhgfg3zgdtzu4w3zxgs4">fatcat:kzgwkxfhgfg3zgdtzu4w3zxgs4</a> </span>
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Page 605 of Mathematical Reviews Vol. , Issue 87b [page]

<span title="">1987</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A typical example is L(V,,), the lattice of r.e. subspaces of an infinite-dimensional computable vector space.  ...  The author studies the groups of recursive automorphisms of con- structive Boolean algebras.  ... 
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Page 3531 of Mathematical Reviews Vol. , Issue 99e [page]

<span title="">1999</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
, Quasi-Heyting algebras: a new class of lattices (115-119); D.  ...  Twareque Ali, Systems of covariance in relativistic quan- tum mechanics (365-373); Michael Keyl, How to describe the space-time structure with nets of C*-algebras (375-385); P.  ... 
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A survey on structural Ramsey theory and topological dynamics with the Kechris-Pestov-Todorcevic correspondence in mind [article]

Lionel Nguyen Van Thé
<span title="2014-12-12">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The purpose of the present paper is to present a self-contained survey of the corresponding developments.  ...  In 2005, Kechris, Pestov and Todorcevic established a surprising correspondence between structural Ramsey theory and topological dynamics.  ...  The universal minimal flow was computed for the automorphism group of the random distributive lattice in [KS12] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1412.3254v2">arXiv:1412.3254v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nlaso4d63zdipiltn4hqbii77i">fatcat:nlaso4d63zdipiltn4hqbii77i</a> </span>
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Transcendental Hodge algebra [article]

Misha Verbitsky
<span title="2017-08-02">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We prove that the direct sum of all transcendental Hodge lattices has a natural algebraic structure, and compute this algebra explicitly for a hyperkahler manifold.  ...  The transcendental Hodge lattice of a projective manifold M is the smallest Hodge substructure in p-th cohomology which contains all holomorphic p-forms.  ...  Million thanks to Pierre Deligne who found an error in the published version of this paper (see the footnote to Definition 3.1).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1512.01011v3">arXiv:1512.01011v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2a7rcdqq6nciblwscms3el6zmq">fatcat:2a7rcdqq6nciblwscms3el6zmq</a> </span>
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Hodge structure of K3 type with real multiplication and Simple Abelian Fourfolds with Definite Quaternionic Multiplication [article]

Yuwei Zhu
<span title="2020-10-25">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we give a general construction of transcendental lattices for K3 surfaces with real multiplication by arbitrary field up to degree 6 along with formula for their discriminants.  ...  field by keeping track of the arithmetic input on both sides.  ...  John Voight on arithmetic properties of Clifford algebras, and Prof. Frank Calegari for pointing to an error in the draft. The author is supported by the NSF grants DMS-1551514 and DMS-1701659.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1906.10157v2">arXiv:1906.10157v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rjwifwvnxzcqno5zumfetqsu2u">fatcat:rjwifwvnxzcqno5zumfetqsu2u</a> </span>
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A Survey On Structural Ramsey Theory And Topological Dynamics With The Kechris-Pestov-Todorcevic Correspondence In Mind

Lionel Nguyen Van Thé
<span title="2015-04-15">2015</span> <i title="Zenodo"> Zenodo </i> &nbsp;
The purpose of the present paper is to present a self-contained survey of the corresponding developments.  ...  SANU, Belgrade ; International audience ; In 2005, Kechris, Pestov and Todorcevic established a surprising correspondence between structural Ramsey theory and topological dynamics.  ...  The universal minimal flow was computed for the automorphism group of the random distributive lattice in [29] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.1471599">doi:10.5281/zenodo.1471599</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hlaz3o7lkzf6dh3sjgxqvfhp7a">fatcat:hlaz3o7lkzf6dh3sjgxqvfhp7a</a> </span>
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K3 surfaces associated to Abelian Fourfolds of Mumford's Type [article]

Yuwei Zhu
<span title="2019-04-15">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Galluzzi showed that the weight 2 Hodge structure of such a variety decomposes into Hodge substructures via the action of Mumford-Tate group, one of which is of K3 type with Hodge number (1,7,1).  ...  Comparing them with the list by Shimada, we will show that the Mordell-Weil group of all elliptic fibrations have either 2-torsion or trivial torsion group, and the conditions of the occurance of 2-torsions  ...  Kiran Kedlaya for pointing to the subject of Mumford's construction, Prof. John Voight for the many helpful and enlightening discussions on the arithmetic properties of quaternion algebras, Prof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1812.06882v2">arXiv:1812.06882v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lgcps4kebvbfjgozpo6u3ym3fe">fatcat:lgcps4kebvbfjgozpo6u3ym3fe</a> </span>
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Fourier's Method of Linear Programming and Its Dual

H. P. Williams
<span title="">1986</span> <i title="JSTOR"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6jb2mei4hzg4vdohokley4c5om" style="color: black;">The American mathematical monthly</a> </i> &nbsp;
Section 32 describing the type of problem) 32K05 Banach analytic Automorphism groups of C n and affine manifolds 32M25 Complex vector fields 32M99 None of the above, but in this section 32Nxx Automorphic  ...  chains 20F24 FC-groups and their generalizations 20F28 Automorphism groups of groups [See also 20E36] 20F29 Representations of groups as automorphism groups of algebraic systems 20F34 Fundamental  ...  Methods of noncommutative geometry [See also 58B34] 83C75 Space-time singularities, cosmic censorship, etc. 83C80 Analogues in lower dimensions 83C99 None of the above, but in this section 83Dxx Relativistic  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2322281">doi:10.2307/2322281</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yvhgyh2epbcwdoqdhuaopkcrue">fatcat:yvhgyh2epbcwdoqdhuaopkcrue</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130603152811/http://www.mathem.pub.ro/dept/MSC-2010.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/af/5d/af5d7893e441e708ed36c71226b8d5031d405fec.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2307/2322281"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> jstor.org </button> </a>

Multicoloured Random Graphs: Constructions and Symmetry [article]

Sam Tarzi
<span title="2014-07-02">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
, rings and algebras, metric spaces, sets and models, Moufang loops and monoids.  ...  We study various aspects of the graphs, but the emphasis is on understanding those groups that are supported by these graphs together with links with other structures such as lattices, topologies and filters  ...  In the setting of vector spaces over finite fields, the Gaussian (or q-binomial) coefficient plays the role of Stirling numbers. Thus there may be a vector space version of the algebra isomorphism.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1406.7870v2">arXiv:1406.7870v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/othjxv7jzbhq7pupvjfmonunva">fatcat:othjxv7jzbhq7pupvjfmonunva</a> </span>
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Master Index To Volumes 11-3011Volumes 11-23 were published under the former name of "Annals of Mathematical Logic"

<span title="">1986</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
Monk, Chains in Boolean algebras Mekler, A.H., Stationary logic of ordinals Mekler, A.H., see Eklof, P.C. Metakides, G. and A. Nerode, Recursively enumerable vector spaces Metakides, G. and A.  ...  Mills, G., Substructure lattices of models of arithmetic Mitchell, W.J., see Jech, T.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0168-0072(86)90026-6">doi:10.1016/0168-0072(86)90026-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lvxcgirz7zcp7if573hj6t7poi">fatcat:lvxcgirz7zcp7if573hj6t7poi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171003225446/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/d44/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMTY4MDA3Mjg2OTAwMjY2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/30/d9/30d9bd07adf4f2f441b1483028ea1ba8fceb72e1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0168-0072(86)90026-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Functional reducts of Boolean algebras [article]

Bertalan Bodor, Kende Kalina, Csaba Szabó
<span title="2020-02-05">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper we classify some special reducts of the countable atomless Boolean algebra which we call functional reducts.  ...  In this case a, b and 1 are linearly independent in the vector space structure, so there is a permutation ϕ in the linear group which fixes the 1 and switches a and b.  ...  In this paper we show that Ba has exactly 13 functional reducts. 11 out of these 13 reducts are reducts of Ba considered as a vector space together with the constant 1 (later denoted by (+ 0 , 0, 1)).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1506.01314v2">arXiv:1506.01314v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zdrv2eqlkbaafglww7vyjcmzay">fatcat:zdrv2eqlkbaafglww7vyjcmzay</a> </span>
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Infinite-dimensional Polish groups and Property (T) [article]

Tomás Ibarlucía
<span title="2020-08-30">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Its main ingredient is the construction, for any ℵ_0-categorical metric structure, of an action of a free group on a system of elementary substructures with suitable independence conditions.  ...  unitary representation of G^∘ without invariant unit vectors restricts to a multiple of the left-regular representation of F.  ...  Moreover, by Proposition 1.2, G • is also the automorphism group of an ℵ 0 -categorical structure, and in the latter every algebraic element is definable.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1903.00203v2">arXiv:1903.00203v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mnxwrzrkjzcdjjnyqkfu5qrt3y">fatcat:mnxwrzrkjzcdjjnyqkfu5qrt3y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200909062443/https://arxiv.org/pdf/1903.00203v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1903.00203v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

The topology of U-duality (sub)groups

Arjan Keurentjes
<span title="2004-03-01">2004</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j5iizqxt2rainmxg6nfmpg2ds4" style="color: black;">Classical and quantum gravity</a> </i> &nbsp;
We discuss the topology of the symmetry groups appearing in compactified (super-)gravity, and discuss two applications.  ...  in a formulation of de Wit-Nicolai type.  ...  P5/27 and in part by the European Commision RTN programme HPRN-CT-2000-00131, in which the author is associated to the University of Leuven.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/0264-9381/21/6/025">doi:10.1088/0264-9381/21/6/025</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7676w3eldvgnrjwtct46zsi6ly">fatcat:7676w3eldvgnrjwtct46zsi6ly</a> </span>
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