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Marco Barone

Queen's University, Belfast
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  •  67
    Undecidability of indecomposable polynomial rings
    with Nicolás Caro-Montoya and Eudes Naziazeno
    Archive for Mathematical Logic 64 (1): 185-203. 2025.
    By using algebraic properties of (commutative unital) indecomposable polynomial rings we achieve results concerning their first-order theory, namely: interpretability of arithmetic and a uniform proof of undecidability of their full theory, both in the language of rings without parameters. This vastly extends the scope of a method due to Raphael Robinson, which deals with a restricted class of polynomial integral domains.
  •  30
    Uniform definability of integers in reduced indecomposable polynomial rings
    with Nicolás Caro and Eudes Naziazeno
    Journal of Symbolic Logic 85 (4): 1376-1402. 2020.
    We prove first-order definability of the prime subring inside polynomial rings, whose coefficient rings are reduced and indecomposable. This is achieved by means of a uniform formula in the language of rings with signature $$. In the characteristic zero case, the claim implies that the full theory is undecidable, for rings of the referred type. This extends a series of results by Raphael Robinson, holding for certain polynomial integral domains, to a more general class.
    Mathematical Logic
  •  173
    The Vacuum as Ether in the Last Century
    Foundations of Physics 34 (12): 1973-1982. 2004.
    In this paper we review the evolution of the concept of “ vacuum ” according to different theories formulated in the last century, like Quantum Mechanics, Quantum Electrodynamics, Quantum Chromodynamics in Particle Physics and Cosmology. In all these theories a metastable vacuum state is considered which transforms from one state to another according to the energy taken into consideration. It is a “fluid” made up by matter and radiation present in the whole Universe, which may be identified with…Read more
    Physics