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  1.  19
    A General Theorem on Temporal Foliations of Causal Sets.Ali Bleybel & Abdallah Zaiour - 2018 - Foundations of Physics 48 (4):456-478.
    Causal sets are a particular class of partially ordered sets, which are proposed as basic models of discrete space-time, specially in the field of quantum gravity. In this context, we show the existence of temporal foliations for any causal set, or more generally, for a causal space. Moreover, we show that automorphisms of a large class of infinite causal sets fall into two classes 1) Automorphisms of spacelike hypersurfaces in some given foliation, or 2) Translations in time. More generally, we (...)
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  2.  25
    The Field of LE-Series with a Nonstandard Analytic Structure.Ali Bleybel - 2011 - Notre Dame Journal of Formal Logic 52 (3):255-265.
    In this paper we prove that the field of Logarithmic-Exponential power series endowed with the exponential function and a class of analytic functions containing both the overconvergent functions in the t -adic norm and the usual strictly convergent power series is o-minimal.
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  3.  24
    P-Adically Closed Fields with Nonstandard Analytic Structure.Ali Bleybel - 2010 - Journal of Symbolic Logic 75 (3):802-816.
    We prove quantifier elimination for the field ${\Bbb Q}_{p}((t^{{\Bbb Q}}))$ (the completion of the field of Puiseux series over ${\Bbb Q}_{p}$ ) in Macintyre's language together with symbols for functions in a class containing both t-adically and p-adically overconvergent functions. We also show that the theory of ${\Bbb Q}_{p}((t^{{\Bbb Q}}))$ is b-minimal in this language.
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