Filters








1,403,333 Hits in 4.9 sec

The theory of concatenation over finite models [article]

Dominik D. Freydenberger, Liat Peterfreund
2021 arXiv   pre-print
We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations.  ...  Like the theory of concatenation, FC is built around word equations; in contrast to it, its semantics are defined to only allow finite models, by limiting the universe to a word and all its factors.  ...  Thusly, the universe of C is always assumed to be Σ * , making all models infinite. We propose FC, the finite model version of the theory of concatenation.  ... 
arXiv:1912.06110v6 fatcat:qs76gsdhxzbrxdlydyl6xkgbcq

Reflections on Finite Model Theory

Phokion G. Kolaitis
2007 22nd Annual IEEE Symposium on Logic in Computer Science (LICS 2007)  
Main Finding: All major computational complexity classes, including P, NP, and PSPACE, can be characterized in terms of definability in various logics on classes of finite structures.  ...  Classical Model theory in the finite: Do the classical results of model theory hold in the finite? The Skolem-Löwenheim Theorem is meaningless in the finite.  ...  model theory.  ... 
doi:10.1109/lics.2007.39 dblp:conf/lics/Kolaitis07 fatcat:3eulyaqcgbfdzihya6kzjxm2ru

Persistently finite theories with hyperarithmetic models

Terrence Millar
1983 Transactions of the American Mathematical Society  
Nerode asked if there could be a complete decidable theory with only finitely many countable models up to isomorphism, such that not all of the countable models were decidable.  ...  It is not difficult to show that any countable model of a hyperarithmetic theory which has only finitely many countable models must be decidable in some hyperarithmetic degree.  ...  A complete theory T is persistently finite if every complete extension in £(£) U {cx,... ,c"} has finitely many countable models up to isomorphism, n < to.  ... 
doi:10.1090/s0002-9947-1983-0697062-8 fatcat:rubfmv44svg3jouisitllglali

Finite Field Theory in Solvable Models

Kozo Kikuchi, Kunio Yamamoto
1971 Progress of theoretical physics  
Recently, a new finite local theory,!> requiring no additional field, has been presented.  ...  The great success of the present renormalization theory suggests that correct finite theory should be the one giving no influence on observable quantities.  ...  Recently, a new finite local theory,!> requiring no additional field, has been presented.  ... 
doi:10.1143/ptp.46.1631 fatcat:eauateblbbh5lghd7do523hnf4

Preservation theorems in finite model theory [chapter]

Eric Rosen, Scott Weinstein
1995 Lecture Notes in Computer Science  
We d e v elop various aspects of the nite model theory of L k (9) a n d L k 1! (9). We establish the optimality of normal forms for L k 1!  ...  Before proceeding to these results, we d e v elop some of the nite model theory of L k (9) a n d L k 1! (9) in the next section. 3 Basic Finite Model Theory for L k (9) and L k 1!  ...  Moreover, each s u c h theory has a nite model. By 5] , every such theory is axiomatized by a single L k sentence.  ... 
doi:10.1007/3-540-60178-3_99 fatcat:ta5q7jzkinc2jfcvr265blwoti

Finite-model theory - a personal perspective

Ronald Fagin
1993 Theoretical Computer Science  
., Finite-mode1 theory -a personal perspective, Theoretical Computer Science 116 (1993) 3-31. Finite-model theory is a study of the logical properties of finite mathematical structures.  ...  This paper is a very personalized view of finite-model theory, where the author focuses on his own personal history, and results and problems of interest to him, especially those springing from work in  ...  to finite-model theory, see [3, pp. 12221261 ).  ... 
doi:10.1016/0304-3975(93)90218-i fatcat:hmpnxjt5bvg37nwy6agiccmlm4

Strong convergence in finite model theory

Wafik Boulos Lotfallah
2002 Journal of Symbolic Logic (JSL)  
AbstractIn [9] we introduced a new framework for asymptotic probabilities, in which a σ-additive measure is defined on the sample space of all sequencesof finite models, where the universe of, is {1,2,  ...  variables, and roughly states that for each formulaϕ(x), the fraction of tuplesain, which satisfy the formulaϕ(x), almost surely has a limit asntends to infinity.We show that the infinitary logic with finitely  ...  Y of all extension axioms is the theory of all sentences of strong uniform measure 1. we have that: Using compactness we get a finite subset Y oc ' 4' . such that From the proof of Theorem 5.3 in [  ... 
doi:10.2178/jsl/1190150151 fatcat:kf5cq7dbtzg2vfgjkomwwddili

Persistently Finite Theories with Hyperarithmetic Models

Terrence Millar
1983 Transactions of the American Mathematical Society  
Nerode asked if there could be a complete decidable theory with only finitely many countable models up to isomorphism, such that not all of the countable models were decidable.  ...  It is not difficult to show that any countable model of a hyperarithmetic theory which has only finitely many countable models must be decidable in some hyperarithmetic degree.  ...  A complete theory T is persistently finite if every complete extension in £(£) U {cx,... ,c"} has finitely many countable models up to isomorphism, n < to.  ... 
doi:10.2307/1999303 fatcat:iyj6feb32ngrlf75uhi5svnggi

Finite Unification: Theory, Models and Predictions [article]

S. Heinemeyer, , G. Zoupanos
2011 arXiv   pre-print
All-loop Finite Unified Theories (FUTs) are very interesting N=1 supersymmetric Grand Unified Theories (GUTs) realising an old field theory dream, and moreover have a remarkable predictive power due to  ...  Here we review FUT models based on the SU(5) and SU(3)^3 gauge groups and their predictions.  ...  In the following we discuss two versions of the all-order finite model: the model of Ref.  ... 
arXiv:1101.2476v1 fatcat:5ixoyg3oefddjbrakhrbvxmava

Finite-model theory—a personal perspective [chapter]

Ronald Fagin
1990 Lecture Notes in Computer Science  
., Finite-mode1 theory -a personal perspective, Theoretical Computer Science 116 (1993) 3-31. Finite-model theory is a study of the logical properties of finite mathematical structures.  ...  This paper is a very personalized view of finite-model theory, where the author focuses on his own personal history, and results and problems of interest to him, especially those springing from work in  ...  to finite-model theory, see [3, pp. 12221261 ).  ... 
doi:10.1007/3-540-53507-1_67 fatcat:bo7ne5kfbbfzdn2gkaw4fy2vbu

Theories of arithmetics in finite models

Michał Krynicki, Konrad Zdanowski
2005 Journal of Symbolic Logic (JSL)  
On the contrary we show that the Σ2–theory of multiplication is undecidable in finite models.  ...  We show that this result is optimal by proving that the Σ1–theory of multiplication and order is decidable in finite models as well as in the standard model.  ...  Undecidable theories of arithmetic in finite models In the present section we are going to describe the properties of a theory which has greater expressive power in finite models than in the standard case  ... 
doi:10.2178/jsl/1107298508 fatcat:vftok4tzfzeejknsqvt2urjo3i

A finite quantum gravity field theory model

Jorge Alfaro, Pablo González, Ricardo Avila
2011 Classical and quantum gravity  
Then we proceed to study the existence of ghosts in the model. Finally, we study the form of the finite quantum corrections to the classical action of the model.  ...  We apply this to General Relativity and we calculate the one loop divergent part of the Effective Action showing its null contribution in vacuum, implying a finite model.  ...  Moreover, the finiteness of string models make plausible the assertion that the model so formulated provides a consistent theory of Quantum Gravity.  ... 
doi:10.1088/0264-9381/28/21/215020 fatcat:hxi44agqn5g67nfxj54k75l5ue

Trakhtenbrot's Theorem in Coq: Finite Model Theory through the Constructive Lens [article]

Dominik Kirst, Dominique Larchey-Wendling
2022 arXiv   pre-print
We study finite first-order satisfiability (FSAT) in the constructive setting of dependent type theory.  ...  As a consequence, finite validity cannot be characterised by a complete finitary deduction system and, resting on finite model theory, various natural problems in database theory and separation logic are  ...  Again, both of these standard results come with their subtleties when explored in a constructive approach to finite model theory.  ... 
arXiv:2104.14445v4 fatcat:rbzzrmzbyfgbxbxumrikgt3yte

On Finitely Generated Models of Theories with at Most Countably Many Nonisomorphic Finitely Generated Models [article]

Abderezak Ould Houcine
2008 arXiv   pre-print
We study finitely generated models of countable theories, having at most countably many nonisomorphic finitely generated models.  ...  of its complete theory.  ...  A finitely generated group G is said H-limit if G is a model of the universal theory of H.  ... 
arXiv:0804.2908v1 fatcat:bd7zb2xnxvccnnn7tlary76c5i

A model of the twisted K-theory related to bundles of finite order [article]

A.V. Ershov
2014 arXiv   pre-print
In the present paper we propose a geometric model of the twisted K-theory corresponding to elements of finite order in H^3(X, Z)× [X, _⊗].  ...  In the present paper we make an attempt to give such a model for elements of finite order in H 3 (X, Z) × [X, BBSU ⊗ ].  ...  We propose this fibration as a model for the twisted K-theory for twistings corresponding to the action of bundles of order k on K(X) by the tensor product (cf. Theorem 24).  ... 
arXiv:1005.3807v9 fatcat:dwwofbj7znauzfizcxryia24uu
« Previous Showing results 1 — 15 out of 1,403,333 results