Use this URL to cite or link to this record in EThOS:
Title: Hyperarithmetical properties of relations on Abelian p-groups and orderings
Author: Barker, Ewan James
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 1992
Availability of Full Text:
Access from EThOS:
Full text unavailable from EThOS. Please try the link below.
Access from Institution:
An r.e. structure A consists of given r.e. relations and recursive functions on a recursive universe. Given another relation R on the structure, we ask whether the structure can be renumbered to form a new (but classically isomorphic) r.e. structure on which the corresponding relation is not a Σα0 set (where α is a constructive ordinal). If this cannot be done, we say that R is intrinsically Σα^0+ on A. If R can be defined by a recursive infinitary formula of a certain kind, involving the given relations and functions of the structure, then we say R is formally Σα^0+. This definition guarantees that R is intrinsically Σα^0+. In this thesis we show that If certain conditions guaranteeing extra decidabilitiy are satisfied, then R is intrinsically Σα^0+if it is formally Σα^0+. The required decidability conditions are established for certain linear orderings and reduced abelian p-groups, and this result is applied to various relations in these cases. Related questions are discussed in the case of the reduced abelian p-groups, and the thesis concludes with an example showing a difference between r.e. and recursive structures.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available