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Linearization of definable order relations

Vladimir Kanovei
2000 Annals of Pure and Applied Logic  
We prove that if ≤ is an analytic partial order then either ≤ can be extended to a (boldface) Δ^1_2 linear order similar to an antichain in 2^<ω_1 ordered lexicographically or a certain Borel partial order  ...  Some corollaries for analytic equivalence relations are given, for instance, if E is a Σ^1_1[z] equivalence relation such that E_0 does not embed in E then E is determined by intersections with E-invariand  ...  Introduction It is a simple application of Zorn's lemma that any partial order can be extended to a linear order on the same domain.  ... 
doi:10.1016/s0168-0072(99)00013-5 fatcat:dj6ko3dstvggdj2mnatlsjwkg4

G-structures of second order defined by linear operators satisfying algebraic relations

D. Demetropoulou-Psomopoulou
1997 Publicacions matemàtiques  
Also, the almost tangent structure of order two is mentioned and its generalisation, the second order almost transverse structure, is defined.  ...  The present work is based on a type of structures on a differential manifold V , called G-structures of the second kind, defined by endomorphism J on the second order tangent bundle T 2 (V ).  ...  A real almost product structure of second order is defined ([5]) on an n-dimensional differentiable manifold V n of class C ∞ , by a linear operator J x acting on the space T 2 x (V n ) of the second order  ... 
doi:10.5565/publmat_41297_09 fatcat:fb3b4p6j4zbmfi6ueabxzkxmfa

On Sequences of Numbers and Polynomials Defined by Linear Recurrence Relations of Order 2

Tian-Xiao He, Peter J.-S. Shiue
2009 International Journal of Mathematics and Mathematical Sciences  
Here we present a new method to construct the explicit formula of a sequence of numbers and polynomials generated by a linear recurrence relation of order 2.  ...  The derived idea provides a general method to construct identities of number or polynomial sequences defined by linear recurrence relations.  ...  Hsu on occasion of his 90th birthday. The authors wish to thank the referees for their helpful comments and suggestions.  ... 
doi:10.1155/2009/709386 fatcat:nkmvyvftyna5bjvzhc4vebkoti

The maximum element order in the groups related to the linear groups which is a multiple of the defining characteristic

M.R. Darafsheh
2008 Finite Fields and Their Applications  
In this paper we find the maximum order of an element of the above groups which is a multiple of p.  ...  Let n be a natural number and q be the power of a prime p. The general, special and projective special linear groups are denoted by GL n (q), SL n (q) and PSL n (q), respectively.  ...  Acknowledgment I would like to thank the research council of the University of Tehran for supporting this research through grant #6101031-1-02.  ... 
doi:10.1016/j.ffa.2008.05.007 fatcat:wwqyzxx6urbdzguczepcc3mgwu

Definability of Combinatorial Functions and Their Linear Recurrence Relations [article]

T. Kotek, J.A. Makowsky
2009 arXiv   pre-print
Many of these functions satisfy a linear recurrence relation over Z or Z_m and allow an interpretation as counting the number of relations satisfying a property expressible in Monadic Second Order Logic  ...  In this paper we give a complete characterization in terms of definability in MSOL of the combinatorial functions which satisfy a linear recurrence relation over Z, and discuss various extensions and limitations  ...  can extend the Specker-Blatter Theorem in terms of order invariance and MSOL-definability.  ... 
arXiv:0907.5420v1 fatcat:m3n44k2zmncufnasiipgmbgpuu

The classification of homogeneous finite-dimensional permutation structures [article]

Samuel Braunfeld, Pierre Simon
2018 arXiv   pre-print
., homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron, and confirming the classification conjectured by the first author.  ...  of linear orders.  ...  Thus, this partial order provides a linear order of C/E for each C ∈ X/F . We call E the bottom relation and F the top relation of the subquotient order.  ... 
arXiv:1807.07110v2 fatcat:gscd5q4whrfldfn73mcxq5tyjm

The Classification of Homogeneous Finite-Dimensional Permutation Structures

Samuel Braunfeld, Pierre Simon
2020 Electronic Journal of Combinatorics  
We classify the homogeneous finite-dimensional permutation structures, i.e. homogeneous structures in a language of finitely many linear orders, giving a nearly complete answer to a question of Cameron  ...  Acknowledgements We would like to thank Gregory Cherlin for looking over some early forms of these results.  ...  of linear orders.  ... 
doi:10.37236/8321 fatcat:ackjg5y4hzbezki5zmmmssaujm

Page 3857 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
The FO normaliz- ability of linear order in 7% is defined in a similar way.  ...  defined by y in (M,<) is a linear ordering of M and does not depend on the choice of <.  ... 

How to define a linear order on finite models

Lauri Hella, Phokion G. Kolaitis, Kerkko Luosto
1997 Annals of Pure and Applied Logic  
We carry out a systematic investigation of the definability of linear order on classes of finite rigid structures.  ...  We obtain upper and lower bounds for the expressibility of linear order in various logics that have been studied extensively in finite model theory, such as least fixpoint logic LFP, partial fixpoint logic  ...  In particular, one of the referees provided the argument for Corollary 3.9, which strengthened a result contained in an earlier version of this paper.  ... 
doi:10.1016/s0168-0072(97)00008-0 fatcat:5h4r4lawurdh5fknxdhrmxbafm

Two Definitions of Fractional Derivative of Powers Functions

Raoelina Andriambololona
2013 Pure and Applied Mathematics Journal  
We consider the set of powers functions defined on and their linear combinations.  ...  After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative integers, positive and negative fractional orders.  ...  But on equal footing as the definitions of "semi-equality" and 'semi-linearity" defined in the relations (3.1.8), (3.1.11) and (3.2.2),we may define the property of "semi-commutativity" for the relation  ... 
doi:10.11648/j.pamj.20130201.12 fatcat:o5lskmmofbht3p3ocvyn7quz3e

Linear orders and semiorders close to an interval order

Marc Roubens, Philippe Vincke
1983 Discrete Applied Mathematics  
The purpose of this paper is to study the properties of the linear orders and semiorders at minimum symmetric difference distance from a given interval order on a finite set.  ...  The following theorem shows that the underlying linear order related to a semiorder close to a given interval order is, in some sense, compatible with the intersection of the underlying linear orders related  ...  Let P be an asymmetric (x Py -+ not y Px) binary relation on X. The symmetric complement of P on X is defined by x ly * not x Py and not y Px.  ... 
doi:10.1016/0166-218x(83)90084-7 fatcat:2x5hgq2itrf7na2usuk64myt44

Does weak quasi-o-minimality behave better than weak o-minimality? [article]

Slavko Moconja, Predrag Tanović
2021 arXiv   pre-print
In particular, we closely describe definable linear orders and prove a weak version of the monotonicity theorem.  ...  We also prove that weak quasi-o-minimality of a theory with respect to one definable linear order implies weak quasi-o-minimality with respect to any other such order.  ...  Suppose that ≺ and ⊳ are definable linear orders, E is a definable ≺convex equivalence relation and R is a definable (≺ E , ⊳)-monotone relation.  ... 
arXiv:1811.05228v4 fatcat:5eee6t74srfh7j6jn77occlywy

An infinitary model of linear logic [article]

Charles Grellois, Paul-André Melliès
2015 arXiv   pre-print
In this paper, we construct an infinitary variant of the relational model of linear logic, where the exponential modality is interpreted as the set of finite or countable multisets.  ...  We then extend the relational semantics with a notion of color or priority in the sense of parity games.  ...  The relational model of linear logic In order to be reasonably self-contained, we briefly recall the relational model of linear logic.  ... 
arXiv:1411.4380v3 fatcat:lxj4n52rqbardkoji5747wv3c4

On the Expressiveness of the Interval Logic of Allen's Relations Over Finite and Discrete Linear Orders [chapter]

Luca Aceto, Dario Della Monica, Anna Ingólfsdóttir, Angelo Montanari, Guido Sciavicco
2014 Lecture Notes in Computer Science  
A complete classification of all HS fragments with respect to their relative expressive power has been recently given for the classes of all linear orders and of all dense linear orders.  ...  The cases of discrete and finite linear orders turn out to be much more involved.  ...  Many classes of linear orders are of practical interest, including the class of all (resp., dense, discrete, finite) linear orders, as well as the particular linear order on R (resp., Q, Z, and N).  ... 
doi:10.1007/978-3-319-11558-0_19 fatcat:zg3fc5venzfyfna4njpyg6jlai

On Choice Sets and Strongly Non-Trivial Self-Embeddings of Recursive Linear Orders

Rodney G. Downey, Michael F. Moses
1989 Mathematical Logic Quarterly  
We use the fact that the successor relation S(a, b) defined by is III in every recursive linear order.  ...  The above-mentioned argument from DUSHNIK and MILLER [1) shows that every recursive linear order (i.e. with universe Nand < a recursive relation) with a recursive subset consisting only of intervals of  ...  (Vx < a) (Vy) (3z > y) ((x -< z -< a) v (a -< z -< x)) defines a choice set. Here < is the order relation of Nand -< that of the recursive linear order in question.  ... 
doi:10.1002/malq.19890350307 fatcat:yfan6r3gnjhqpcckeo2kjnh5ii
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