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Ioannis Souldatos

  1. Characterizing the powerset by a complete (Scott) sentence.

    Thu, 05/17/2012 - 15:01 — SomNambul
    Authors: Ioannis Souldatos
    Subjects: Logic
    Abstract

    This paper is part II of a study on cardinals that are characterizable by a
    Scott sentence, continuing the work from this http URL A
    cardinal $\kappa$ is characterized by a Scott sentence $\phi_\M$, if $\phi_\M$
    has a model of size $\kappa$, but no model of $\kappa^+$.

  2. Every set of first-order formulas is equivalent to an independent set.

    Mon, 08/29/2011 - 15:01 — SomNambul
    Authors: Ioannis Souldatos, I. Reznikoff
    Subjects: Logic
    Abstract

    A set of first-order formulas, whatever the cardinality of the set of
    symbols, is equivalent to an independent set.

  3. Notes on cardinals that are characterizable by a complete (Scott) sentence.

    Fri, 07/16/2010 - 15:01 — SomNambul
    Authors: Ioannis Souldatos
    Subjects: Logic
    Abstract

    We study which cardinals are characterizable by a Scott sentence, in the
    sense that $\phi_M$ characterizes $\kappa$, if it has a model of size $\kappa$,
    but not of $\kappa^+$. We show that if $\aleph_\alpha$ is characterizable by a
    Scott sentence and $\beta<\omega_1$, then $\aleph_{\alpha+\beta}$ is
    characterizable by a Scott sentence.

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