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Page 756 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
.], thus contributes to the al- most complete solution of the important question of asymptotic probabilities of logically definable properties over sparse random graphs.  ...  More specifically, the author and Spencer showed [“Nonconvergence for sparse random graphs”, submitted] that the probability of an infinitary formula with k +2 variables may asymptotically not converge  ... 

Page 2970 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
Glass (Cambridge) 99e:03026 03C75 03C13 03C65 Lynch, James F. (1-CKSN-CS; Potsdam, NY) Infinitary logics and very sparse random graphs. (English summary) J. Symbolic Logic 62 (1997), no. 2, 609-623.  ...  Let p(n) be the edge probability of the random graph on n vertices. It is shown that if p(n) <n!  ... 

Page 4015 of Mathematical Reviews Vol. , Issue 2003f [page]

2003 Mathematical Reviews  
The result has also been proved for first-order logic under probability distributions other than the uniform one, in particular for sparse random graphs [S. Shelah and J. H. Spencer, J. Amer. Math.  ...  It has been proved for more expressive logics, such as the fixed-point logics and the infinitary logic Y>5.— which extends first-order logic with infinitary conjunctions and disjunctions while allowing  ... 

Page 7536 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
fixed point logic PFP, infinitary logic Y@., with a finite number of variables, and the closures of these logics under implicit definition.  ...  The third offers an analysis of rigidity (giving equivalent conditions for bounded rigidity, and treating infinitary logic with counting quan- tifiers).  ... 

JSL volume 62 issue 2 Cover and Front matter

1997 Journal of Symbolic Logic (JSL)  
VARDI 608 Infinitary logics and very sparse random graphs, by JAMES F.  ...  The JOURNAL and the BULLETIN are the official organs of the Association for Symbolic Logic, an international organization for furthering research in symbolic logic and exchange of ideas among mathematicians  ... 
doi:10.1017/s0022481200016236 fatcat:7s6n5wdax5fgdb2bc7loh37b5i

Strong convergence in finite model theory

Wafik Boulos Lotfallah
2002 Journal of Symbolic Logic (JSL)  
, and further characterize the measures on random graphs for which the strong convergence law holds.  ...  satisfy the formulaϕ(x), almost surely has a limit asntends to infinity.We show that the infinitary logic with finitely many variables has the strong convergence law for formulas for the uniform measure  ...  Keisler for his guidance and precious advice throughout the paper. Some of the ideas of the paper were inspired by a probability course I audited with J.  ... 
doi:10.2178/jsl/1190150151 fatcat:kf5cq7dbtzg2vfgjkomwwddili

Page 2257 of Mathematical Reviews Vol. , Issue 94d [page]

1994 Mathematical Reviews  
Lynch, Infinitary logics and very sparse random graphs (191-198); Guy Fayolle, Stéphane Grumbach and Christophe Tollu, Asymptotic probabilities of languages with generalized quantifiers (199-207); Moreno  ...  ); Beverly Jamison and Stephan Olariu, On the homogeneous decomposition of graphs (170-183); Sajal K.  ... 

Page 4448 of Mathematical Reviews Vol. , Issue 95h [page]

1995 Mathematical Reviews  
sparse unary predicates.  ...  The logic EBTL al- lows one to reason both about the current state, represented by a node of the graph, as well as about paths that lead from the root to the current state, or from the latter to infinity  ... 

Randomisation and Derandomisation in Descriptive Complexity Theory

Kord Eickmeyer, Martin Grohe, Anuj Dawar
2011 Logical Methods in Computer Science  
Our main focus lies on questions of derandomisation, and we prove that there is a query which is definable in BPFO, the probabilistic version of first-order logic, but not in Cinf, finite variable infinitary  ...  This implies that many of the standard logics of finite model theory, like transitive closure logic and fixed-point logic, both with and without counting, cannot be derandomised.  ...  Acknowledgements We would like to thank Nicole Schweikardt and Dieter van Melkebeek for helpful comments on an earlier version of this paper.  ... 
doi:10.2168/lmcs-7(3:14)2011 fatcat:ez6mz5hh3fcoda6ka726764rre

An Analytic Approach to Sparse Hypergraphs: Hypergraph Removal [article]

Henry Towsner
2018 arXiv   pre-print
We use this framework to give a proof of hypergraph removal for sub-hypergraphs of sparse random hypergraphs.  ...  The use of tools from analysis to approach problems in graph theory has become an active area of research.  ...  Introduction In this paper we bring together two recent trends in extremal graph theory: the study of "sparse random" analogs of theorems about dense graphs, and the use of methods from analysis and logic  ... 
arXiv:1204.1884v5 fatcat:2nz4f74uwrf6plga6xuqd2ccnu

Strong modeling limits of graphs with bounded tree-width [article]

Andrzej Grzesik, Daniel Kráľ, Samuel Mohr
2022 arXiv   pre-print
The notion of first order convergence of graphs unifies the notions of convergence for sparse and dense graphs. Nešetřil and Ossona de Mendez [J.  ...  Symbolic Logic 84 (2019), 452–472] proved that every first order convergent sequence of graphs from a nowhere-dense class of graphs has a modeling limit and conjectured the existence of such modeling limits  ...  Acknowledgement The authors would like to thank both anonymous reviewers for their detailed and insightful comments, which have helped to significantly improve the presentation of the arguments given in  ... 
arXiv:2103.10354v3 fatcat:pzb2wkzkdbeyvkuej32jrmtga4

On digraph coloring problems and treewidth duality

Albert Atserias
2008 European journal of combinatorics (Print)  
Using this, we illustrate the power of the logical approach to CSPs by resolving two conjectures about treewidth duality in the digraph case.  ...  The combination of this result with an older result by Nešetřil and Tardif shows that there is a computable listing of all template structures whose CSP is definable in full first-order logic.  ...  Acknowledgement We thank Phokion Kolaitis, Jarik Nešetřil, and the referees of LICS 2005 for useful comments.  ... 
doi:10.1016/j.ejc.2007.11.004 fatcat:euiy3glnynhpvar6nzaif74nnq

k --Universal Finite Graphs [article]

Eric Rosen, Saharon Shelah, Scott Weinstein
1996 arXiv   pre-print
This paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics.  ...  The main results of the paper, which are due to Shelah, establish that the class of k-universal graphs is not definable by an infinite disjunction of first-order existential sentences with a finite number  ...  The class of k-extendible graphs plays an important role in the study of 0 − 1 laws for certain infinitary logics and logics with fixed point operators (see [KV92] ).  ... 
arXiv:math/9604244v1 fatcat:ukavb7yl4fdcze57nh4io425cm

Evolving Shelah-Spencer Graphs [article]

Richard Elwes
2019 arXiv   pre-print
The strange logic of random graphs (Vol. 22). Springer Science Business Media.] and throughout the model-theoretic literature.  ...  We analyse the graphs that result from this process, including the infinite limit, in comparison to Shelah-Spencer sparse random graphs discussed in [Spencer, J., 2013.  ...  the random graph).  ... 
arXiv:1809.08333v2 fatcat:z6kq7gz4kjep3fxrwqdtlhpcte

JSL volume 62 issue 4 Cover and Back matter and Errata

1997 Journal of Symbolic Logic (JSL)  
use of its methods; and (4) studies in the history of logic.  ...  The JOURNAL and the BULLETIN are the official organs of the Association for Symbolic Logic, an international organization for furthering research in logic and exchange of ideas among mathematicians, computer  ...  Infinitary logics and very sparse random graphs 609 MACPHERSON, DUGALD. See HASKELL, DEIRDRE. MAGIDOR, MENACHEM. See FOREMAN, MATTHEW. MAKOWSKY, J. A. See ADAMEK, J.  ... 
doi:10.1017/s0022481200015565 fatcat:5fra5p2djfa2lilfcnzigmb5ea
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