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The subdirect decomposition theorem for classes of structures closed under direct limits

Xavier Caicedo
1980 Journal of the Australian Mathematical Society  
In this paper we show that this result is true for any class of structures, not necessarily algebraic, closed under isomorphisms and direct limits.  ...  Birkhoff, every algebra in an equationally defined class of algebras K is a subdirect product of subdirectly irreducible algebras of K.  ...  Malcev( 1971) has shown that a class K is a quasivariety if and only if it is closed under direct limits, products, and substructures (see Eklof (1975) for an elegant proof), in this case the decomposition  ... 
doi:10.1017/s1446788700016463 fatcat:tmtkjshpwzbeblef6bhl42ap24

Fraïssé limits of limit groups [article]

Olga Kharlampovich, Alexei Myasnikov, Rizos Sklinos
2019 arXiv   pre-print
We modify the notion of a Fraïssé class and show that various interesting classes of groups, notably the class of nonabelian limit groups and the class of finitely generated elementary free groups, admit  ...  Fraïssé limits.  ...  A A; • (N2) if A B C, then A C; • (N3) if A C and A ⊆ B ⊆ C, then A B. • (IP) the class K is closed under isomorphisms; • ( -HP) the class K is closed under finitely generated elementary -substructures  ... 
arXiv:1807.08131v2 fatcat:e7jxqmhswzgfxkxdkwegk26kxe

Free amalgamation and automorphism groups [article]

Andreas Baudisch
2014 arXiv   pre-print
If free amalgamation for finitely generated substructures exits in N, then it is a stationary independece relation in the sense of K.Tent and M.Ziegler [TZ12b].  ...  Let L be a countable elementary language, N be a Fraisse limit. We consider free amalgamation for L-structures where L is arbitrary.  ...  Let J be the class of the substructures of the models of T h(M 0 ). If K is closed under free amalgamation, then J is closed under free amalgamation.  ... 
arXiv:1406.1130v1 fatcat:64h6arvaa5cd5mkqgp7o5jdgqa

Automorphism groups and Ramsey properties of sparse graphs

David M. Evans, Jan Hubička, Jaroslav Nešetřil
2019 Proceedings of the London Mathematical Society  
We investigate amenable and extremely amenable subgroups of these groups using the space of orientations of the graph and results from structural Ramsey theory.  ...  We study automorphism groups of sparse graphs from the viewpoint of topological dynamics and the Kechris, Pestov, Todorčević correspondence.  ...  Assume that S is closed under composition and contains all isomorphisms.  ... 
doi:10.1112/plms.12238 fatcat:trv2g76rnrbbjjnm5ly5oj7rxa

A Reiterman theorem for pseudovarieties of finite first-order structures

J. -E. Pin, P. Weil
1996 Algebra Universalis  
Abstract We extend Reiterman's theorem to first-order structures: a class of finite first-order structures is a pseudovariety if and only if it is defined by a set of identities in a certain relatively  ...  Nousétendons le théorème de Reiterman aux structures du premier ordre : une classe de structures du premier ordre finies est une pseudovariété si et seulement si elle est définie par un ensemble d'identités  ...  We say that a class of L-structures is a quasivariety if it is closed under taking substructures, direct products and ultraproducts.  ... 
doi:10.1007/bf01243597 fatcat:jdcmx5d2nve3to436q7wrjdp44

Abstract elementary classes and accessible categories

T. Beke, J. Rosický
2012 Annals of Pure and Applied Logic  
elementary class Accessible category We investigate properties of accessible categories with directed colimits and their relationship with categories arising from Shelah's Abstract Elementary Classes.  ...  The connection between abstract elementary classes and accessible categories was discovered, independently, by M.J. Lieberman as well; see [7] and [8].  ...  A nearly full subcategory K of Emb(Σ) is called an abstract elementary class if it is closed in Emb(Σ) under directed colimits and there is a cardinal λ such that if f : A → B is a substructure with B  ... 
doi:10.1016/j.apal.2012.06.003 fatcat:3q74a4w3h5hxtc7q63gw4u4umi

New Ramsey Classes from Old [article]

Manuel Bodirsky
2012 arXiv   pre-print
Let C_1 and C_2 be strong amalgamation classes of finite structures, with disjoint finite signatures sigma and tau.  ...  We also discuss variations of this statement, and give several examples of new Ramsey classes derived from those general results.  ...  Many thanks to François Bossière, Jan Foniok, András Pongrácz, and Miodrag Sokić for their valuable comments on earlier versions of this text.  ... 
arXiv:1204.3258v2 fatcat:jt2qx6x76vc7znkrxptgug2oli

Universal homogeneous event structures and domains

Manfred Droste
1991 Information and Computation  
We also show that the category of all event domains is closed under inverse limits. Similar results are derived for Kahn and Plotkin's concrete data structures and concrete domains. pl  ...  A class % of L-structures is called isomorphism-closed, if & g $8 and d E %? imply B E %?, and hereditary, if V is closed under taking substructures. % has the d~%? with &,zG? and G!  ...  INVERSE LIMITS OF EVENT DOMAINS In this section we prove that each of the categories 9, &, %?9, gd, 9&, %?9,, is closed under inverse limits.  ... 
doi:10.1016/0890-5401(91)90032-w fatcat:cgl43mm7hnclvd4ppxm6fsbdby

Universal abstract elementary classes and locally multipresentable categories

Michael Lieberman, Jiří Rosický, Sebastien Vasey
2018 Proceedings of the American Mathematical Society  
We similarly give an equivalence between abstract elementary classes (AECs) admitting intersections and locally polypresentable categories.  ...  We exhibit an equivalence between the model-theoretic framework of universal classes and the category-theoretic framework of locally multipresentable categories.  ...  K is a µ-universal class if: (1) K is a class of structures in a fixed µ-ary vocabulary τ = τ (K). (2) K is closed under isomorphism, unions of µ-directed systems of τ -substructure inclusions, and τ -  ... 
doi:10.1090/proc/14326 fatcat:ad4vczf3krf4dnrnz6ew4iqvqy

Structural logic and abstract elementary classes with intersections

Will Boney, Sebastien Vasey
2019 Bulletin of the Polish Academy of Sciences Mathematics  
We give a syntactic characterization of abstract elementary classes (AECs) closed under intersections using a new logic with a quantifier for isomorphism types that we call structural logic: we prove that  ...  This generalizes Tarski's syntactic characterization of universal classes.  ...  Baldwin, Marcos Mazari-Armida, and the referee for feedback which helped improve the presentation of this paper.  ... 
doi:10.4064/ba8178-12-2018 fatcat:yummhk4alze5nfi3nwpwhtbuoe

Existentially closed structures in the power of the continuum

Donato Giorgetta, Saharon Shelah
1984 Annals of Pure and Applied Logic  
Now either class is closed under taking unions of chains. By an appropriate choice of the language L we can ensure that both classes are also closed under taking substructures.  ...  Let 3'l be either the class of locally finite groups or any class of L-structures which is closed under taking substructures and unions of chains and has free amalgamation and HNN-extensions.  ...  . -* (fa',_&,, E B, and thus a;'(fa;?i). . * a;'(fa;-') E B, and we can apply the induction assumption. Therefore g2,k w[a', b'] = 1.  ... 
doi:10.1016/0168-0072(84)90013-7 fatcat:h67ep7qzcnf67alcpfldeznf2e

Abstract elementary classes and accessible categories [article]

Tibor Beke, Jiri Rosicky
2011 arXiv   pre-print
We compare abstract elementary classes of Shelah with accessible categories having directed colimits.  ...  A nearly full subcategory K of Emb(Σ) is called an abstract elementary class if it is closed in Emb(Σ) under directed colimits and there is a cardinal λ such that if f : A → B is a substructure with B  ...  A nearly full subcategory K of Emb(Σ) is an abstract elementary class if and only if it is an accessible category closed under directed colimits in Emb(Σ).  ... 
arXiv:1005.2910v2 fatcat:ewjdxud2nnbu5ei6efbjutbz7y

Axiomatizing AECs and applications [article]

Samson Leung
2021 arXiv   pre-print
For any abstract elementary class (AEC) K with λ=LS( K), the following holds: 1. K has an axiomatization in L_(2^λ)^+,λ^+, allowing game quantification.  ...  These extend Kueker's result which assumes finite character and λ=ℵ_0. 2. If K is universal and categorical in λ, then it is axiomatizable in L_λ^+,λ^+. 3.  ...  Proof. 1. σ ≤ (x) requires that x is closed under functions. 2.  ... 
arXiv:2108.09708v2 fatcat:ppe4eijwjrb4bammcfiw5flhoq

Page 11 of Mathematical Reviews Vol. 42, Issue 1 [page]

1971 Mathematical Reviews  
A concrete class of formulae closed under strong homomorphism is pointed out.”’ (Armenian. Russian and English Waszkiewicz, Jan A remark on ’s filter-images. Colloq. Math. 21 (1970), 165-167.  ...  Three additional, increasingly wider classes of relation theoretic operations are defined whose members give rise to inclusions of the above type whenever the A,’s are replaced by various closed sets of  ... 

Finite Element Study of Hyperstructure Systems with Modular Light-Frame Construction in High-Rise Buildings

Nicolas Labrecque, Sylvain Ménard, Marc Oudjene, Pierre Blanchet
2022 Buildings  
The interaction between both systems and the impact on the substructures were analyzed.  ...  The analysis indicates that the system could be viable, but more research should be especially performed on the connections between the substructures and the hyperstructure.  ...  Space for the construction site is very limited, neighbors are close and can be bothered by the noise and dust, and arteries closure can have increased consequences the longer the construction lasts for  ... 
doi:10.3390/buildings12030330 fatcat:x2okyknzsvavtj7wendbqjxlhe
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