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  1. Computable axiomatizability of elementary classes.Peter Sinclair - 2016 - Mathematical Logic Quarterly 62 (1-2):46-51.
    The goal of this paper is to generalise Alex Rennet's proof of the non‐axiomatizability of the class of pseudo‐o‐minimal structures. Rennet showed that if is an expansion of the language of ordered fields and is the class of pseudo‐o‐minimal ‐structures (‐structures elementarily equivalent to an ultraproduct of o‐minimal structures) then is not computably axiomatizable. We give a general version of this theorem, and apply it to several classes of structures.
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  • Additive Covers and the Canonical Base Property.Michael Loesch - 2023 - Journal of Symbolic Logic 88 (1):118-144.
    We give a new approach to the failure of the Canonical Base Property (CBP) in the so far only known counterexample, produced by Hrushovski, Palacín and Pillay. For this purpose, we will give an alternative presentation of the counterexample as an additive cover of an algebraically closed field. We isolate two fundamental weakenings of the CBP, which already appeared in work of Chatzidakis and Moosa-Pillay and show that they do not hold in the counterexample. In order to do so, a (...)
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