Abstract
In this paper we investigate the question of existence of a jump inversion structure for a given structure \(\mathcal{A}\) in the context of their respective degree spectra and the sets definable in them by computable infinitary formulae. More specifically, for a countable structure \(\mathcal{A}\) and a computable successor ordinal α, we show that we can apply the construction from [4] to build a structure \(\mathcal{N}_\alpha\) such that the sets definable in \(\mathcal{A}\) by \(\Sigma^{c,\Delta^0_\alpha}_1\) formulae are exactly the sets definable in \(\mathcal{N}_\alpha\) by \(\Sigma^{c}_{\alpha}\) formulae.
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Vatev, S. (2013). Another Jump Inversion Theorem for Structures. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds) The Nature of Computation. Logic, Algorithms, Applications. CiE 2013. Lecture Notes in Computer Science, vol 7921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39053-1_49
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DOI: https://doi.org/10.1007/978-3-642-39053-1_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39052-4
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