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

2004
*
International journal of algebra and computation
*

McKenzie, we prove that there

doi:10.1142/s0218196704001748
fatcat:qqoa3wi2jffwlhz7au5nlqtlxe
*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. ...##
###
Some model theory of Bezout difference rings- a survey

2007
*
Bulletin of the Belgian Mathematical Society Simon Stevin
*

Under an addition assumption on K, we will show that the "module" theory of R

doi:10.36045/bbms/1170347806
fatcat:fhgbfvhzszbrfpwaclry4ertoq
*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 ...##
###
On a question of Abraham Robinson's
[article]

2013
*
arXiv
*
pre-print

In this note we give

arXiv:1309.7138v2
fatcat:ro3zzys6mvef3cm2fhs74gllv4
*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 ...##
###
A field guide to equational logic

1992
*
Journal of symbolic computation
*

The concept of

doi:10.1016/0747-7171(92)90013-t
fatcat:ou4teabieffhhlciea4odb546i
*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 . ...##
###
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]

1977
*
Lecture Notes in Computer Science
*

Definition 13: The

doi:10.1007/3-540-08342-1_30
fatcat:xggoyhew2zdnvehpvwbgfhx7v4
*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. ...##
###
Some results about exponential fields (survey)

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). ...

##
###
A Perfect-Information Construction for Coordination in Games

2011
*
Foundations of Software Technology and Theoretical Computer Science
*

The construction yields an infinite game tree with epistemic

doi:10.4230/lipics.fsttcs.2011.387
dblp:conf/fsttcs/BerwangerKP11
fatcat:5nfwpehwgraevfeern54uubzki
*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. ...##
###
Higher-Order Linear Differential Systems with Truncated Coefficients
[chapter]

2011
*
Lecture Notes in Computer Science
*

. ∞ i=0 Ξ u (i)x i

doi:10.1007/978-3-642-23568-9_2
fatcat:ktuedgckvfhszncafbuyefwwrq
*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*. ...##
###
On the Question of Absolute Undecidability

2006
*
Philosophia Mathematica
*

For example, it

doi:10.1093/philmat/nkj009
fatcat:uhxexcfcjzc6raotuwu6rbc5y4
*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 ...##
###
Decidable Equational Classes
[chapter]

1997
*
Algebraic Model Theory
*

I will discuss the progress that

doi:10.1007/978-94-015-8923-9_10
fatcat:mmny623nebbhpkrpfrs3lrxjc4
*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. ...##
###
A well-structured framework for analysing petri net extensions

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*. ...

##
###
A Simple Logic of Functional Dependence

2021
*
Journal of Philosophical Logic
*

Various language extensions are presented as well, up to

doi:10.1007/s10992-020-09588-z
fatcat:yt6oioavrrfkbkvbo3pfwgw3ja
*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 ...##
###
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]

2019
*
arXiv
*
pre-print

It

arXiv:1904.01407v1
fatcat:f7difxg7ozcivma5okdbyusnmi
*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*. ...
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