Kalfa, Kornilia (1980)
Decision problems concerning sets of equations.
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This thesis is about "decision problems concerning properties of sets of equations".
If L is a first-order language with equality and if P is a property of sets of L-equations, then "the decision problem of P in L" is the problem of the existence or not of an algorithm, which enables us to decide whether, given a set Sigma of L-equations, Sigma has the property P or not. If such an algorithm exists, P is decidable in L. Otherwise, it is undecidable in L.
After surveying the work that has been done in the field, we present a new method for proving the undecidability of a property P, for finite sets of L-equations. As an application, we establish the undecidability of some basic model-theoretical properties, for finite sets of equations of non-trivial languages. Then, we prove the non-existence of an algorithm for deciding whether a field is finite and, as a corollary, we derive the undecidability of certain properties, for recursive sets of equations of infinite non-trivial languages. Finally, we consider trivial languages, and we prove that a number of properties, undecidable in languages with higher complexity, are decidable in them.
This is a Accepted version
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is not peer reviewed
Deposited by David Morgan (UBYL020) on
in Royal Holloway Research Online.Last modified on 06-Feb-2017
Digitised in partnership with ProQuest, 2015-2016.
Institution: University of London, Bedford College (United Kingdom).