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Preservation theorems in finite model theory
[chapter]

1995
*
Lecture Notes in Computer Science
*

We d e v elop various aspects of the nite

doi:10.1007/3-540-60178-3_99
fatcat:ta5q7jzkinc2jfcvr265blwoti
*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*. ...##
###
The Theory of Finite Models without Equal Sign

2005
*
Acta Mathematica Sinica. English series
*

Compactness

doi:10.1007/s10114-005-0537-1
fatcat:pokm6nu2nfeolotdrixrpmz45q
*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. ...##
###
Reflections on Finite Model Theory

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

doi:10.1109/lics.2007.39
dblp:conf/lics/Kolaitis07
fatcat:3eulyaqcgbfdzihya6kzjxm2ru
*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*. ...##
###
Gabriel–Ulmer duality and Lawvere theories enriched over a general base

2009
*
Journal of functional programming
*

We develop a body of

doi:10.1017/s0956796809007254
fatcat:fw7mim6kfrggvazkfkiscetcb4
*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. ...##
###
Generalizations of the Los-Tarski Preservation Theorem
[article]

2013
*
arXiv
*
pre-print

For arbitrary

arXiv:1302.4350v2
fatcat:we3ock3knnaelmbrq2z3yly774
*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*. ...##
###
Higher Lawvere theories
[article]

2019
*
arXiv
*
pre-print

Our main result establishes a universal property for the infinity category of Lawvere

arXiv:1903.02991v1
fatcat:jj53tu24k5grvc3gak773qrd4u
*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. ...##
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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. ...##
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The universal finite set
[article]

2018
*
arXiv
*
pre-print

; the set is empty

arXiv:1711.07952v2
fatcat:zihb3ucpdjfbrb5m3crckrd2vu
*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*. ...##
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Free finitary algebras in a co-complete cartesian closed category

1972
*
Canadian mathematical bulletin
*

We want to show that his proof remains valid if instead of set valued

doi:10.4153/cmb-1972-068-9
fatcat:44xeamfgebafjdu6c3tdhq7eey
*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 ...##
###
The Grothendieck ring of varieties and algebraic K-theory of spaces
[article]

2016
*
arXiv
*
pre-print

Waldhausen's algebraic K-

arXiv:1611.09327v1
fatcat:43gw6vzqfnexfj6tbopp3iy6ky
*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. ...##
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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. ...##
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A Generalization of the Łoś-Tarski Preservation Theorem - Dissertation Summary
[article]

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*. ...

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

2016
*
arXiv
*
pre-print

Previous work of the author [39] showed that the Homomorphism

arXiv:1612.08192v1
fatcat:y23tkqrz6bhwxmslgtmswmew2a
*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 ...##
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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 ...##
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Distal systems in topological dynamics and ergodic theory
[article]

2022
*
arXiv
*
pre-print

We show that such a

arXiv:2202.03456v2
fatcat:ifgyu7q53vapngbay3lezqnqzu
*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*...
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