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The subdirect decomposition theorem for classes of structures closed under direct limits
1980
Journal of the Australian Mathematical Society
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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]
2019
arXiv
pre-print
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2018 pre-print arXiv:1807.08131v1 fatcat:giiqsbin4fhhhkryic2v7qxtvu
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]
2014
arXiv
pre-print
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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
2019
Proceedings of the London Mathematical Society
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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
1996
Algebra Universalis
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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
2012
Annals of Pure and Applied Logic
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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]
2012
arXiv
pre-print
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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
1991
Information and Computation
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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
2018
Proceedings of the American Mathematical Society
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2018 pre-print arXiv:1707.09005v3 fatcat:kvougtfqvndqtcyqogxmjhyddiOther Versions
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
2019
Bulletin of the Polish Academy of Sciences Mathematics
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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
1984
Annals of Pure and Applied Logic
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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]
2011
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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
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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
2022
Buildings
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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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