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  1. An Ehrenfeucht‐Fraïssé game for Lω1ω.Jouko Väänänen & Tong Wang - 2013 - Mathematical Logic Quarterly 59 (4-5):357-370.
    In this paper we develop an Ehrenfeucht‐Fraïssé game for. Unlike the standard Ehrenfeucht‐Fraïssé games which are modeled solely after the behavior of quantifiers, this new game also takes into account the behavior of connectives in logic. We prove the adequacy theorem for this game. We also apply the new game to prove complexity results about infinite binary strings.
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  • An infinte natural sum.Paolo Lipparini - 2016 - Mathematical Logic Quarterly 62 (3):249-257.
    As far as algebraic properties are concerned, the usual addition on the class of ordinal numbers is not really well behaved; for example, it is not commutative, nor left cancellative etc. In a few cases, the natural Hessenberg sum is a better alternative, since it shares most of the usual properties of the addition on the naturals. A countably infinite iteration of the natural sum has been used in a recent paper by Väänänen and Wang, with applications to infinitary logics. (...)
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  • Some Results on Series of Ordinals.J. L. Hickman - 1976 - Mathematical Logic Quarterly 23 (1‐6):1-18.
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  • Some Results on Series of Ordinals.J. L. Hickman - 1977 - Mathematical Logic Quarterly 23 (1-6):1-18.
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  • The Rise of non-Archimedean Mathematics and the Roots of a Misconception I: The Emergence of non-Archimedean Systems of Magnitudes.Philip Ehrlich - 2006 - Archive for History of Exact Sciences 60 (1):1-121.
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  • Intermediate arithmetic operations on ordinal numbers.Harry J. Altman - 2017 - Mathematical Logic Quarterly 63 (3-4):228-242.
    There are two well‐known ways of doing arithmetic with ordinal numbers: the “ordinary” addition, multiplication, and exponentiation, which are defined by transfinite iteration; and the “natural” (or “Hessenberg”) addition and multiplication (denoted ⊕ and ⊗), each satisfying its own set of algebraic laws. In 1909, Jacobsthal considered a third, intermediate way of multiplying ordinals (denoted × ), defined by transfinite iteration of natural addition, as well as the notion of exponentiation defined by transfinite iteration of his multiplication, which we denote. (...)
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