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DETERMINING WHETHER ${\mathsf V}({\bf A})$ HAS A MODEL COMPANION IS UNDECIDABLE

ROSS WILLARD
2004 International journal of algebra and computation  
McKenzie, we prove that there is no algorithm which, given a finite algebra in a finite language, determines whether the variety (equational class) generated by the algebra has a model companion.  ...  In particular, there exists a finite algebra such that the variety it generates has no model companion; this answers a question of Burris and Werner from 1979. 1991 Mathematics Subject Classification.  ...  The problem of deciding, given a description of a finite algebra A in a finite language, whether V(A) has a model companion is recursively unsolvable. Proof.  ... 
doi:10.1142/s0218196704001748 fatcat:qqoa3wi2jffwlhz7au5nlqtlxe

Some model theory of Bezout difference rings- a survey

Françoise Point
2007 Bulletin of the Belgian Mathematical Society Simon Stevin  
Under an addition assumption on K, we will show that the "module" theory of R has a model-companion.  ...  A theory T is decidable if there is a fixed algorithm which, given a property P expressed in the language of T , determines whether P is a theorem of T . • To show decidability of a theory T , one can  ...  K is a model of T w , 2. the residue field k has characteristic 0, 3 . no residual σ-identities: for every p[X] ∈ k[X]σ − {0}, there is an element a ∈ k with p(a) = 0, 4. genericity axiom: for any inhomogeneous  ... 
doi:10.36045/bbms/1170347806 fatcat:fhgbfvhzszbrfpwaclry4ertoq

On a question of Abraham Robinson's [article]

Jochen Koenigsmann
2013 arXiv   pre-print
In this note we give a negative answer to Abraham Robinson's question whether a finitely generated extension of an undecidable field is always undecidable.  ...  We also construct undecidable algebraic extensions of Q that allow decidable finite extensions.  ...  By a small variation of Theorem 27.2.3 of [FJ] , T R,0 has a model companion T R,0 whose models are ω-free PAC-fields of characteristic 0 with algebraic part F alg ('ω-free' means that any countable elementary  ... 
arXiv:1309.7138v2 fatcat:ro3zzys6mvef3cm2fhs74gllv4

A field guide to equational logic

George F. McNulty
1992 Journal of symbolic computation  
The concept of a ring is ordinarily presented by saying that a ring is a system (R, +, -, , 0,1) in which the following equations are true : A ring is an algebra-meaning here a nonempty set endowed with  ...  By way of this relation each equational theory-that is, each set of equations closed under logical consequence-is associated with a variety of algebras : the class of all algebras in which each equation  ...  There is an algorithm for determining whether a finite semigroup is inherently nonfinitely based .  ... 
doi:10.1016/0747-7171(92)90013-t fatcat:ou4teabieffhhlciea4odb546i

Page 7671 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
companion; (3) if T has a model with the finite cover property then 7, has no model completion.  ...  7671 admits quantifier elimination, then the model companion of T, (if it exists) is a simple theory. The author shows that, under certain conditions on 7, the theory 7, has no model companion.  ... 

Simple programs and their decision problems [chapter]

A. Pnueli, G. Slutzki
1977 Lecture Notes in Computer Science  
Definition 13: The Determinism Problem (DP), for some class of programs, is to decide whether a given P in the class is determistic, i.e. for every input there exists at most one computation path induced  ...  Z ÷ Z+y START .... > V(q3) = 5 Fig. i The motivation for studying the FSLP model and its extensions is (at least) twofold.  ... 
doi:10.1007/3-540-08342-1_30 fatcat:xggoyhew2zdnvehpvwbgfhx7v4

Some results about exponential fields (survey)

Helmut Wolter
1984 Mémoires de la Société mathématique de France  
V* ^ 3x(E*(x) = a Our results show that the theory of EF is rather complicated and since EF has models with quite different properties, EP is not a good approximation of Th(R,e).  ...  It is an open question whether this property is true for all terms and it is also open whether OEF' proves Th^(R,e). Theorem 12. [DW2] Let (P,E,E*) be a model of OEPp . (i).  ... 
doi:10.24033/msmf.315 fatcat:fxdaug5dpvhajfh3auh2hz23zm

A Perfect-Information Construction for Coordination in Games

Dietmar Berwanger, Lukasz Kaiser, Bernd Puchala, Marc Herbstritt
2011 Foundations of Software Technology and Theoretical Computer Science  
The construction yields an infinite game tree with epistemic models associated to nodes.  ...  The abstraction generates finite game graphs in several relevant cases, and leads to a new semi-decision procedure for multi-player games with imperfect information.  ...  equivalent companion model q(K) ≈ K.  ... 
doi:10.4230/lipics.fsttcs.2011.387 dblp:conf/fsttcs/BerwangerKP11 fatcat:5nfwpehwgraevfeern54uubzki

Higher-Order Linear Differential Systems with Truncated Coefficients [chapter]

S. A. Abramov, M. A. Barkatou, E. Pflügel
2011 Lecture Notes in Computer Science  
. ∞ i=0 Ξ u (i)x i is given. This is factually a model of computation. Our results can be represented without using this model (skipping the undecidability questions then), see Remark 1.  ...  We consider the following problem: given a linear differential system with formal Laurent series coefficients, we want to decide whether the system has non-zero Laurent series solutions, and find all such  ...  (i) The algorithmic problem of recognizing whether or not a given system of the form (1) has a solution in k((x)) m \ {0} is undecidable.  ... 
doi:10.1007/978-3-642-23568-9_2 fatcat:ktuedgckvfhszncafbuyefwwrq

On the Question of Absolute Undecidability

P. Koellner
2006 Philosophia Mathematica  
For example, it has bearing on whether in the scenario discussed at the end of §4 there is a substantive issue in deciding between V = L[E] and V = L[E] [G] .  ...  He then says that he can prove that "[e]ither A is absolutely undecidable or Cantor's continuum hypothesis is demonstrable" but that he has "not been able to determine which of these two possibilities  ... 
doi:10.1093/philmat/nkj009 fatcat:uhxexcfcjzc6raotuwu6rbc5y4

Decidable Equational Classes [chapter]

Matthew A. Valeriote
1997 Algebraic Model Theory  
I will discuss the progress that has been made on solving two open problems dealing with the decidability of the first order theory of equationally defined classes of algebras (varieties).  ...  As a result we have the following corollary: Corollary 3.1 If V is a locally finite equational class and is stable (or has few models in some infinite cardinal) then V = V 1 ⊗V 2 where V 1 is a strongly  ...  It has been known for some time that V is undecidable, but I would like to indicate how a local analysis of Z 4 using tame congruence theory can help.  ... 
doi:10.1007/978-94-015-8923-9_10 fatcat:mmny623nebbhpkrpfrs3lrxjc4

A well-structured framework for analysing petri net extensions

Alain Finkel, Pierre McKenzie, Claudine Picaronny
2004 Information and Computation  
whether F gives rise to a WSN is undecidable, a consequence of Rice's theorem [25] which we state as Proposition 7.1: Nevertheless, in concrete cases, it is generally known or easy to decide in which  ...  We could give partial results with other kinds of hypotheses (AB = B which captures the Petri net model, {A n | n ∈ ‫}ގ‬ is a finite set which captures the transfer Petri net model. . .).  ...  The cost of such a computation is therefore bound- A.  ... 
doi:10.1016/j.ic.2004.01.005 fatcat:hnrm462p2fcalhrajtrywhocpi

A Simple Logic of Functional Dependence

Alexandru Baltag, Johan van Benthem
2021 Journal of Philosophical Logic  
Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models.  ...  AbstractThis paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities  ...  Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long  ... 
doi:10.1007/s10992-020-09588-z fatcat:yt6oioavrrfkbkvbo3pfwgw3ja

Page 913 of Mathematical Reviews Vol. , Issue 83c [page]

1983 Mathematical Reviews  
The Post correspondence problem of length n (PCP(n) for short) is to determine whether there is a word in =* with g(w)=h(w).  ...  One would try to find as small as possible u such that PCP(u) is undecidable and as large as possible d such that PCP(d) is decidable. A result of Yu. V.  ... 

On Transitive modal many-valued logics [article]

Amanda Vidal
2019 arXiv   pre-print
It is shown that a large family of those logics -- including the ones arising from the standard MV and Product algebras -- yields an undecidable consequence relation.  ...  We conclude the article by showing the undecidability of the validity and the local SAT questions over transitive models when the Delta operation is added to the logic.  ...  The problem of determining whether ϕ follows locally from Γ in 4K A is undecidable. Moreover, also the problem of determining whether ϕ follows locally from Γ in ω4K A is undecidable.  ... 
arXiv:1904.01407v1 fatcat:f7difxg7ozcivma5okdbyusnmi
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