Displaying similar documents to “A family of 2 ℵ 1 logarithmic functions of distinct growth rates”

Levelled O-minimal structures.

David Marker, Chris Miller (1997)

Revista Matemática de la Universidad Complutense de Madrid

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We introduce the notion of leveled structure and show that every structure elementarily equivalent to the real expo field expanded by all restricted analytic functions is leveled.

On the jump number of lexicographic sums of ordered sets

Hyung Chan Jung, Jeh Gwon Lee (2003)

Czechoslovak Mathematical Journal

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Let Q be the lexicographic sum of finite ordered sets Q x over a finite ordered set P . For some P we can give a formula for the jump number of Q in terms of the jump numbers of Q x and P , that is, s ( Q ) = s ( P ) + ∑ x ∈ P s ( Q x ) , where s ( X ) denotes the jump number of an ordered set X . We first show that w ( P ) - 1 + ∑ x ∈ P s ( Q x ) ≤ s ( Q ) ≤ s ( P ) + ∑ x ∈ P s ( Q x ) , where w ( X ) denotes the width of an ordered set X . Consequently, if P is a Dilworth ordered set, that is, s ( P ) = w ( P ) - 1 , then the formula holds. We also show that it holds again if P is bipartite. Finally, we prove that the lexicographic...

Divisibility in certain automorphism groups

Ramiro H. Lafuente-Rodríguez (2007)

Czechoslovak Mathematical Journal

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We study solvability of equations of the form x n = g in the groups of order automorphisms of archimedean-complete totally ordered groups of rank 2. We determine exactly which automorphisms of the unique abelian such group have square roots, and we describe all automorphisms of the general ones.

Relatively complete ordered fields without integer parts

Mojtaba Moniri, Jafar S. Eivazloo (2003)

Fundamenta Mathematicae

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We prove a convenient equivalent criterion for monotone completeness of ordered fields of generalized power series [ [ F G ] ] with exponents in a totally ordered Abelian group G and coefficients in an ordered field F. This enables us to provide examples of such fields (monotone complete or otherwise) with or without integer parts, i.e. discrete subrings approximating each element within 1. We include a new and more straightforward proof that [ [ F G ] ] is always Scott complete. In contrast, the Puiseux...