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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!  ...  We i n troduce a generalized notion of preservation theorem and establish some positive results concerning \generalized preservation theorems" for rst-order de nable classes of nite structures which are  ...  Introduction In this paper we i n vestigate the status of preservation theorems in nite model theory.  ... 
doi:10.1007/3-540-60178-3_99 fatcat:ta5q7jzkinc2jfcvr265blwoti

The Theory of Finite Models without Equal Sign

Li Bo Luo
2005 Acta Mathematica Sinica. English series  
Compactness Theorem. 6 ) 6 THEOREMS IN GENERAL MODEL THEORY WHICH ARE ALSO TRUE IN FINITE MODEL THEORY Keisler).  ...  Exercise 5. 2. 6. (9) POSITIVE RESULTS IN FINITE MODEL THEORY We prove the following theorems. Theorem L. 3.  ... 
doi:10.1007/s10114-005-0537-1 fatcat:pokm6nu2nfeolotdrixrpmz45q

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.  ...  Finite model theory has had a constant presence in LICS. At least five times the Kleene Award for Best Student Paper has been given for work in finite model theory.  ... 
doi:10.1109/lics.2007.39 dblp:conf/lics/Kolaitis07 fatcat:3eulyaqcgbfdzihya6kzjxm2ru

Gabriel–Ulmer duality and Lawvere theories enriched over a general base

STEPHEN LACK, JOHN POWER
2009 Journal of functional programming  
We develop a body of theory at this level of generality, in particular explaining how the relationship between generalised Lawvere theories and monads extends Gabriel-Ulmer duality.  ...  Motivated by the search for a body of mathematical theory to support the semantics of computational effects, we first recall the relationship between Lawvere theories and monads on Set.  ...  A model of a Lawvere theory L in a category C with finite products is a finite-product preserving functor from L to C.  ... 
doi:10.1017/s0956796809007254 fatcat:fw7mim6kfrggvazkfkiscetcb4

Generalizations of the Los-Tarski Preservation Theorem [article]

Abhisekh Sankaran, Bharat Adsul, Supratik Chakraborty
2013 arXiv   pre-print
For arbitrary finite vocabularies, we also generalize the extensional version of the Los-Tarski preservation theorem for theories. We also present an interpolant-based approach towards these results.  ...  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  ...  Introduction Preservation theorems in first order logic (henceforth called FO) have been extensively studied in model theory.  ... 
arXiv:1302.4350v2 fatcat:we3ock3knnaelmbrq2z3yly774

Higher Lawvere theories [article]

John D. Berman
2019 arXiv   pre-print
Our main result establishes a universal property for the infinity category of Lawvere theories, which completely characterizes the relationship between a Lawvere theory and its infinity category of models  ...  theories and module Lawvere theories.  ...  An algebra or model of L in C is a functor L Ñ C which preserves finite products.  ... 
arXiv:1903.02991v1 fatcat:jj53tu24k5grvc3gak773qrd4u

Page 409 of Mathematical Reviews Vol. 52, Issue 2 [page]

1976 Mathematical Reviews  
A map of Horn theories is a finite limit preserving functor between abstract Horn theories that preserves the cogenerator. The induced functor between the categories of models has an adjoint.  ...  The finiteness of the rank a, of the theory T (Theorem 1.1) is proved for almost categorical theories T.  ... 

The universal finite set [article]

Joel David Hamkins, W. Hugh Woodin
2018 arXiv   pre-print
; the set is empty in any transitive model and others; and if φ defines the set y in some countable model M of ZFC and y z for some finite set z in M, then there is a top-extension of M to a model N in  ...  Using the universal finite set, we prove that the validities of top-extensional set-theoretic potentialism, the modal principles valid in the Kripke model of all countable models of set theory, each accessing  ...  Maximal Σ 2 theories The existence of the universal finite set provided by the main theorem has a bearing on the question of maximal Σ 2 theories in models of set theory.  ... 
arXiv:1711.07952v2 fatcat:zihb3ucpdjfbrb5m3crckrd2vu

Free finitary algebras in a co-complete cartesian closed category

C. Howlett, D. Schumacher
1972 Canadian mathematical bulletin  
We want to show that his proof remains valid if instead of set valued models of an r-ary theory models of a finitary theory with values in an arbitrary cocomplete cartesian closed category are considered  ...  In [2] Volger proved that the underlying functor of a category of set-valued models of an r-ary theory has a left adjoint.  ...  We want to show that his proof remains valid if instead of set valued models of an r-ary theory models of a finitary theory with values in an arbitrary cocomplete cartesian closed category are considered  ... 
doi:10.4153/cmb-1972-068-9 fatcat:44xeamfgebafjdu6c3tdhq7eey

The Grothendieck ring of varieties and algebraic K-theory of spaces [article]

Oliver Röndigs
2016 arXiv   pre-print
Waldhausen's algebraic K-theory machinery is applied to motivic homotopy theory, producing an interesting motivic homotopy type.  ...  All results except the ones listed in Section 6 were obtained before 2010.  ...  I thank Lars Hesselholt and Marc Levine for discussions and encouragement after talks I gave on the subject in 2011 and 2015, respectively.  ... 
arXiv:1611.09327v1 fatcat:43gw6vzqfnexfj6tbopp3iy6ky

Page 3548 of Mathematical Reviews Vol. , Issue 2004e [page]

2004 Mathematical Reviews  
2004e:03065 as many preservation and interpolation theorems.  ...  What happens to various ‘metamathematical’ theorems, such as preservation and interpolation theorems, over the class of finite structures [see Y.  ... 

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

Abhisekh Sankaran
2018 arXiv   pre-print
In particular, our results show that (natural finitary adaptations of) both the upward and downward versions of the Löwenheim-Skolem theorem from classical model theory can be recovered in a variety of  ...  These include the connections of the model-theoretic notions introduced in the thesis with fixed parameter tractability and notions in the structure theory of sparse graph classes.  ...  Amongst the earliest areas of study in classical model theory, is a class of results called preservation theorems.  ... 
arXiv:1811.01014v1 fatcat:vurmh3kcrbgtve7yp6lqngflpy

An Improved Homomorphism Preservation Theorem From Lower Bounds in Circuit Complexity [article]

Benjamin Rossman
2016 arXiv   pre-print
Previous work of the author [39] showed that the Homomorphism Preservation Theorem of classical model theory remains valid when its statement is restricted to finite structures.  ...  Formally, we show the following: if a first-order sentence Φ of quantifier-rank k is preserved under homomorphisms on finite structures, then it is equivalent on finite structures to an existential-positive  ...  The new proof in this paper of the Homomorphism Preservation Theorem on Finite Structures using AC 0 lower bounds is easily to imply the following "Homomorphism Preservation Theorem for (non-uniform) AC  ... 
arXiv:1612.08192v1 fatcat:y23tkqrz6bhwxmslgtmswmew2a

Page 6064 of Mathematical Reviews Vol. , Issue 2001I [page]

2001 Mathematical Reviews  
Summary: “We prove the following preservation theorem for the Horn fragment of equality-free logic: Theorem 0.1.  ...  This is done in different frameworks: inside a fixed model, without any assumption about saturation, in certain classes of models, where the compactness theorem fails, and in the class of all models of  ... 

Distal systems in topological dynamics and ergodic theory [article]

Nikolai Edeko, Henrik Kreidler
2022 arXiv   pre-print
We show that such a model can, in fact, be chosen completely canonically.  ...  This hinges on a new characterization of isometric extensions in topological dynamics.  ...  As shown by Zimmer (see [Zim76, Theorem 8.7] ) this classical result has an analogue for distal systems in ergodic theory which had beed introduced earlier by Parry in [Par68] : A measure-preserving  ... 
arXiv:2202.03456v2 fatcat:ifgyu7q53vapngbay3lezqnqzu
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