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Preservation under Substructures modulo Bounded Cores [article]

Abhisekh Sankaran, Bharat Adsul, Vivek Madan, Pritish Kamath, Supratik Chakraborty
2012 arXiv   pre-print
We call this property preservation under substructures modulo bounded cores, and present a syntactic characterization via Σ_2^0 sentences for properties of arbitrary structures definable by FO sentences  ...  We investigate a model-theoretic property that generalizes the classical notion of "preservation under substructures".  ...  Finally, many thanks to Nutan Limaye and Akshay Sundararaman for discussions on inexpressibility proofs using preservation theorems.  ... 
arXiv:1205.1358v3 fatcat:24zngbq3ezcfhfkbnbczpze5xy

Preservation under Substructures modulo Bounded Cores [chapter]

Abhisekh Sankaran, Bharat Adsul, Vivek Madan, Pritish Kamath, Supratik Chakraborty
2012 Lecture Notes in Computer Science  
We call this property preservation under substructures modulo bounded cores, and present a syntactic characterization via Σ 0 2 sentences for properties of arbitrary structures definable by FO sentences  ...  We investigate a model-theoretic property that generalizes the classical notion of "preservation under substructures".  ...  Finally, many thanks to Nutan Limaye and Akshay Sundararaman for discussions on inexpressibility proofs using preservation theorems.  ... 
doi:10.1007/978-3-642-32621-9_22 fatcat:qodjazjqw5hwrhxdykw66qy6ju

Generalizations of the Los-Tarski Preservation Theorem [article]

Abhisekh Sankaran, Bharat Adsul, Supratik Chakraborty
2013 arXiv   pre-print
As special cases of our results, we obtain the classical Los-Tarski preservation theorem for sentences in both its extensional and substructural versions.  ...  Finally, we present partial results towards generalizing to theories, the substructural version of the Los-Tarski theorem and in the process, we give a preservation theorem that provides a semantic characterization  ...  The present work builds on notions introduced earlier in [6] , specifically, those of cores and substructures modulo bounded cores.  ... 
arXiv:1302.4350v2 fatcat:we3ock3knnaelmbrq2z3yly774

Equations in oligomorphic clones and the Constraint Satisfaction Problem for ω-categorical structures [article]

Libor Barto, Michael Kompatscher, Miroslav Olšák, Trung Van Pham, Michael Pinsker
2018 arXiv   pre-print
when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain non-trivial linear identity modulo outer embeddings.  ...  We then prove that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a non-trivial system of linear identities  ...  Approaching this problem, we are going to show that under the assumption of finite boundedness, and stronger identities than the Siggers identity modulo outer embeddings, we can derive the satisfaction  ... 
arXiv:1612.07551v3 fatcat:nipnkh3cj5fsxezuqcmvuwjxwi

A Generalization of the Łoś-Tarski Preservation Theorem [article]

Abhisekh Sankaran
2016 arXiv   pre-print
This property, that we call the *Equivalent Bounded Substructure Property*, abbreviated EBSP, intuitively states that a large structure contains a small "logically similar" substructure.  ...  Further, EBSP remains preserved under various well-studied operations, such as complementation, transpose, the line-graph operation, disjoint union, cartesian and tensor products, etc.  ...  Our properties, that we call preservation under substructures modulo k-cruxes and preservation under k-ary covered extensions are exactly the classical properties of preservation under substructures and  ... 
arXiv:1609.06297v1 fatcat:6kucahkypzet3mm3kxpwjhu7py

Cores over Ramsey structures [article]

Antoine Mottet, Michael Pinsker
2021 arXiv   pre-print
We prove that if an ω-categorical structure has an ω-categorical homogeneous Ramsey expansion, then so does its model-complete core.  ...  Is the class of first-order reducts of a finitely bounded homogeneous structures closed under taking model-complete cores?  ...  obtain that the class of first-order reducts of finitely bounded homogeneous Ramsey structures is closed under taking model-complete cores.  ... 
arXiv:2004.05936v3 fatcat:6svz53dna5gddbsncxwqlkxmby

A Generalization of the Łoś-Tarski Preservation Theorem over Classes of Finite Structures [article]

Abhisekh Sankaran, Bharat Adsul, Supratik Chakraborty
2014 arXiv   pre-print
We investigate a generalization of the Łoś-Tarski preservation theorem via the semantic notion of preservation under substructures modulo k-sized cores.  ...  The first is based on well-quasi-ordering under the embedding relation. The second is a logic-based combinatorial property that strictly generalizes the first.  ...  The notion of a class of τ -structures being preserved under substructures modulo bounded cores was introduced in [11]. This notion is central to our work.  ... 
arXiv:1401.5953v1 fatcat:ics7vg5langgri2qp6ygvto23q

A Dichotomy for First-Order Reducts of Unary Structures [article]

Manuel Bodirsky, Antoine Mottet
2017 arXiv   pre-print
Many natural decision problems can be formulated as constraint satisfaction problems for reducts A of finitely bounded homogeneous structures.  ...  We apply our new tractability conditions to prove the general tractability conjecture of Bodirsky and Pinsker for reducts of finitely bounded homogeneous structures for the class C.  ...  We can assume that the model-complete core B of A is a substructure of A.  ... 
arXiv:1601.04520v5 fatcat:psjkbouz6fhzdgprwfthjinje4

On First-Order Definable Colorings [article]

Jaroslav Nesetril
2014 arXiv   pre-print
It has been proved in [3] that the extension preservation theorem holds in any class C that is wide, hereditary (i.e. closed under taking substructures) and closed under disjoint unions, for instance  ...  hereditary classes with bounded degree that are closed under disjoint unions.  ... 
arXiv:1403.1995v2 fatcat:httpf736xzfrjmgsfjpyhh7ecq

Finite Relation Algebras with Normal Representations [article]

Manuel Bodirsky
2018 arXiv   pre-print
As we will see, the concepts of finite boundedness and homogeneity are conditions that have already been studied in the relation algebra literature. 4.1. Finite boundedness.  ...  A class of finite τ -structures that contains at most countably many non-isomorphic structures, has the amalgamation property, and is closed under taking induced substructures and isomorphisms is called  ... 
arXiv:1810.13335v1 fatcat:2tbrfyvyi5e5thdxk7ylebllwq

On first-order definable colorings [chapter]

Jaroslav Nešetřil, Patrice Ossona de Mendez
2014 Geometry, Structure and Randomness in Combinatorics  
It has been proved in [3] that the extension preservation theorem holds in any class C that is wide, hereditary (i.e. closed under taking substructures) and closed under disjoint unions, that is hereditary  ...  classes with bounded degree which are closed under disjoint unions.  ... 
doi:10.1007/978-88-7642-525-7_6 fatcat:g2aoxe3jbncwpgevvzzdwcyz6a

Smooth approximations and CSPs over finitely bounded homogeneous structures [article]

Antoine Mottet, Michael Pinsker
2021 arXiv   pre-print
A relational structure B is called finitely bounded if its age, i.e., its finite induced substructures up to isomorphism, is given by a finite set F of forbidden finite substructures: that is, its age  ...  We claim that every nonempty binary symmetric relation R invariant under Pol(A, 0) contains a pseudoloop modulo Aut(Q; <, 0).  ... 
arXiv:2011.03978v5 fatcat:wt46ufzc7bhvfirnwdx3kejmva

Universal Structures and the logic of Forbidden Patterns

Florent Madelaine, R. Ramanujam
2009 Logical Methods in Computer Science  
bounded expansion) any FPP becomes a CSP.  ...  However, we show that when the input is connected and belongs to a class which has low tree-depth decomposition (e.g. structure of bounded degree, proper minor closed class and more generally class of  ...  Tree-depth and Cores. We show that a coloured structure K of bounded tree-depth has a core of bounded size.  ... 
doi:10.2168/lmcs-5(2:13)2009 fatcat:oe25lkzruzbdnasr7ac2jktgkm

Universal Structures and the Logic of Forbidden Patterns [chapter]

Florent Madelaine
2006 Lecture Notes in Computer Science  
In particular, our result covers input restrictions such as: structures of bounded degree, planar graphs, structures of bounded tree-width and, more generally, classes definable by at least one forbidden  ...  Tree-depth and Cores. We show that a coloured structure K of bounded tree-depth has a core of bounded size.  ...  Then, we show that coloured structures of bounded tree-depth have bounded cores.  ... 
doi:10.1007/11874683_31 fatcat:v3iuqwkbnrdwrp6lfly3jackyu

Relativised homomorphism preservation at the finite level [article]

Lucy Ham
2015 arXiv   pre-print
In contrast to the negative results for algebras, we establish a finite-level relativised homomorphism preservation theorem in the relational case.  ...  In this article, we investigate the status of the homomorphism preservation property amongst restricted classes of finite relational structures and algebraic structures.  ...  classes of bounded treewidth, and more generally, classes of finite structures whose cores exclude at least one minor.  ... 
arXiv:1510.05354v1 fatcat:xcmduwitrfgvdjgactxc4a6fnu
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