The Experts below are selected from a list of 195 Experts worldwide ranked by ideXlab platform

Alexander Zapryagaev - One of the best experts on this subject based on the ideXlab platform.

  • Multi-Dimensional Interpretations of Presburger Arithmetic in Itself.
    arXiv: Logic, 2020
    Co-Authors: Fedor Pakhomov, Alexander Zapryagaev
    Abstract:

    Presburger Arithmetic is the True Theory of natural numbers with addition. We study interpretations of Presburger Arithmetic in itself. The main result of this paper is that all self-interpretations are definably isomorphic to the trivial one. Here we consider interpretations that might be multi-dimensional. We note that this resolves a conjecture by A. Visser. In order to prove the result we show that all linear orderings that are interpretable in $(\mathbb{N};+)$ are scattered orderings with the finite Hausdorff rank and that the ranks are bounded in the terms of the dimensions of the respective interpretations.

  • Interpretations of Linear Orderings in Presburger Arithmetic
    arXiv: Logic, 2019
    Co-Authors: Alexander Zapryagaev
    Abstract:

    Presburger Arithmetic $\mathop{\mathbf{PrA}}\nolimits$ is the True Theory of natural numbers with addition. We consider linear orderings interpretable in Presburger Arithmetic and establish various necessary and sufficient conditions for interpretability depending on dimension $n$ of interpretation. We note this problem is relevant to the interpretations of Presburger Arithmetic in itself, as well as the characterization of automatic orderings. For $n=2$ we obtain the complete criterion of interpretability.

  • LFCS - Interpretations of presburger arithmetic in itself(
    Logical Foundations of Computer Science, 2017
    Co-Authors: Alexander Zapryagaev, Fedor Pakhomov
    Abstract:

    Presburger arithmetic \(\mathop {\mathbf {PrA}}\nolimits \) is the True Theory of natural numbers with addition. We study interpretations of \(\mathop {\mathbf {PrA}}\nolimits \) in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in \((\mathbb {N},+)\) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of \(\mathop {\mathbf {PrA}}\nolimits \) it follows that \(\mathop {\mathbf {PrA}}\nolimits \) isn’t one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.

  • Interpretations of Presburger Arithmetic in Itself
    arXiv: Logic, 2017
    Co-Authors: Alexander Zapryagaev, Fedor Pakhomov
    Abstract:

    Presburger arithmetic PrA is the True Theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.

  • Interpretations in Presburger Arithmetic
    2017
    Co-Authors: Alexander Zapryagaev, Fedor Pakhomov
    Abstract:

    Presburger arithmetic PrA is the True Theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the result we show that all linear orders that are interpretable in (N,+) are scattered orders with finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.

Fedor Pakhomov - One of the best experts on this subject based on the ideXlab platform.

  • Multi-Dimensional Interpretations of Presburger Arithmetic in Itself.
    arXiv: Logic, 2020
    Co-Authors: Fedor Pakhomov, Alexander Zapryagaev
    Abstract:

    Presburger Arithmetic is the True Theory of natural numbers with addition. We study interpretations of Presburger Arithmetic in itself. The main result of this paper is that all self-interpretations are definably isomorphic to the trivial one. Here we consider interpretations that might be multi-dimensional. We note that this resolves a conjecture by A. Visser. In order to prove the result we show that all linear orderings that are interpretable in $(\mathbb{N};+)$ are scattered orderings with the finite Hausdorff rank and that the ranks are bounded in the terms of the dimensions of the respective interpretations.

  • LFCS - Interpretations of presburger arithmetic in itself(
    Logical Foundations of Computer Science, 2017
    Co-Authors: Alexander Zapryagaev, Fedor Pakhomov
    Abstract:

    Presburger arithmetic \(\mathop {\mathbf {PrA}}\nolimits \) is the True Theory of natural numbers with addition. We study interpretations of \(\mathop {\mathbf {PrA}}\nolimits \) in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in \((\mathbb {N},+)\) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of \(\mathop {\mathbf {PrA}}\nolimits \) it follows that \(\mathop {\mathbf {PrA}}\nolimits \) isn’t one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.

  • Interpretations of Presburger Arithmetic in Itself
    arXiv: Logic, 2017
    Co-Authors: Alexander Zapryagaev, Fedor Pakhomov
    Abstract:

    Presburger arithmetic PrA is the True Theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.

  • Interpretations in Presburger Arithmetic
    2017
    Co-Authors: Alexander Zapryagaev, Fedor Pakhomov
    Abstract:

    Presburger arithmetic PrA is the True Theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the result we show that all linear orders that are interpretable in (N,+) are scattered orders with finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.

P. Orekhovsky - One of the best experts on this subject based on the ideXlab platform.

Jacqueline Van Kampen - One of the best experts on this subject based on the ideXlab platform.

  • Towards a Theory of Language Acquisition
    Lot Occasional Series, 2020
    Co-Authors: Jacqueline Van Kampen
    Abstract:

    "We have seen at the workshop a diversity of measurements and a no less diverse amount of different phenomena. Shared areas were acquisition phenomena in Romance languages and more general: the beginnings for a True Theory of language acquisition. I will not attempt to evaluate the various contributions here. All of this must get its time to sink in. Yet, the general point of our endeavors, - the Theory of language acquisition -, may be underlined to gain a further outlook"

Ivan Samson - One of the best experts on this subject based on the ideXlab platform.

  • The birth of the political economy or the economy in the heart of politics
    2020
    Co-Authors: Jacques Fontanel, Jean‐paul Hebert, Ivan Samson
    Abstract:

    Mercantilism is a set of precepts concerning economic policy. It places the State at the heart of national economic development. Wealth is conceived as serving power. Mercantilists share a static conception of international economic relations, considering that one country can only enrich itself to the detriment pf another. It is a True Theory of economic war. However the development of mercantilism shows a progressive transition of economic towards a lower consideration of political aspects.

  • THE BIRTH OF THE POLITICAL ECONOMY OR THE ECONOMY IN THE HEART OF POLITICS: MERCANTILISM
    Defence and Peace Economics, 2008
    Co-Authors: Jacques Fontanel, Jean‐paul Hebert, Ivan Samson
    Abstract:

    Mercantilism (16th-18th centuries) is a set of precepts concerning economic policy. It places the State at the heart of national economic development. Wealth is conceived as serving power. Mercantilists share a static conception of international economic relations, considering that one country can only enrich itself to the detriment of another. It is a True Theory of economic war. However, the development of mercantilism shows a progressive transition of economic thought towards a lower consideration of political aspects.