Use this URL to cite or link to this record in EThOS: | https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.259093 |
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Title: | Decision problems concerning sets of equations | ||||||
Author: | Kalfa, Kornilia |
ISNI:
0000 0001 3594 0666
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Awarding Body: | University of London | ||||||
Current Institution: | Royal Holloway, University of London | ||||||
Date of Award: | 1980 | ||||||
Availability of Full Text: |
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Abstract: | |||||||
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.
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Supervisor: | Not available | Sponsor: | Not available | ||||
Qualification Name: | Thesis (Ph.D.) | Qualification Level: | Doctoral | ||||
EThOS ID: | uk.bl.ethos.259093 | DOI: | Not available | ||||
Keywords: | Mathematics | ||||||
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