Abstract
In the present paper we investigate a relation, called conservative extension, between abstract structures \(\mathfrak{A}\) and \(\mathfrak{B}\), possibly with different signatures and \(\vert\mathfrak{A}\vert\subseteq \vert\mathfrak{B}\vert\). We give a characterisation of this relation in terms of computable Σ n formulae and we show that in some sense it provides a finer complexity measure than the one given by degree spectra of structures. As an application, we show that the n-th jump of a structure and its Marker’s extension are conservative extensions of the original structure.
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Vatev, S. (2011). Conservative Extensions of Abstract Structures. In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_32
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DOI: https://doi.org/10.1007/978-3-642-21875-0_32
Publisher Name: Springer, Berlin, Heidelberg
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