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1 -Boolean spectrum, and stability

Piero Mangani, Annalisa Marcja (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dimostra che la conoscenza delle algebre di Boole dei definibili di modelli di cardinità 1 di una teoria elementare è sufficiente per decidere il suo tipo di stabilità.

Categoricity of theories in Lκω , when κ is a measurable cardinal. Part 1

Saharon Shelah, Oren Kolman (1996)

Fundamenta Mathematicae

We assume a theory T in the logic L κ ω is categorical in a cardinal λ κ, and κ is a measurable cardinal. We prove that the class of models of T of cardinality < λ (but ≥ |T|+κ) has the amalgamation property; this is a step toward understanding the character of such classes of models.

Categoricity without equality

H. Jerome Keisler, Arnold W. Miller (2001)

Fundamenta Mathematicae

We study categoricity in power for reduced models of first order logic without equality.

Characterizing the powerset by a complete (Scott) sentence

Ioannis Souldatos (2013)

Fundamenta Mathematicae

This paper is part II of a study on cardinals that are characterizable by a Scott sentence, continuing previous work of the author. A cardinal κ is characterized by a Scott sentence ϕ if ϕ has a model of size κ, but no model of size κ⁺. The main question in this paper is the following: Are the characterizable cardinals closed under the powerset operation? We prove that if β is characterized by a Scott sentence, then 2 β + β is (homogeneously) characterized by a Scott sentence, for all 0 < β₁ < ω₁....

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