Functorial equations for lexicographic products

Franz Viktor Kuhlmann; Salma Kuhlmann; Saharon Shelah

doi:10.1090/S0002-9939-03-06830-8

Functorial equations for lexicographic products

Franz Viktor Kuhlmann^*
, Salma Kuhlmann
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We generalize the main result of an earlier paper by the authors (Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 (1997), 3177-3183) concerning the convex embeddings of a chain Γ in a lexicographic power Δ^Γ. For a fixed non-empty chain Δ, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functorial equations (Δ^Γ)^≤0 ≃ Γ, (Δ ^Γ)^≤0 ≃ Γ and (Δ ^Γ)^≤0 ≃ Γ.

Original language	English
Pages (from-to)	2969-2976
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	131
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-03-06830-8
State	Published - Oct 2003

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title = "Functorial equations for lexicographic products",

abstract = "We generalize the main result of an earlier paper by the authors (Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 (1997), 3177-3183) concerning the convex embeddings of a chain Γ in a lexicographic power ΔΓ. For a fixed non-empty chain Δ, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functorial equations (ΔΓ)≤0 ≃ Γ, (Δ Γ)≤0 ≃ Γ and (Δ Γ)≤0 ≃ Γ.",

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AU - Kuhlmann, Salma

AU - Shelah, Saharon

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N2 - We generalize the main result of an earlier paper by the authors (Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 (1997), 3177-3183) concerning the convex embeddings of a chain Γ in a lexicographic power ΔΓ. For a fixed non-empty chain Δ, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functorial equations (ΔΓ)≤0 ≃ Γ, (Δ Γ)≤0 ≃ Γ and (Δ Γ)≤0 ≃ Γ.

AB - We generalize the main result of an earlier paper by the authors (Exponentiation in power series fields, Proc. Amer. Math. Soc. 125 (1997), 3177-3183) concerning the convex embeddings of a chain Γ in a lexicographic power ΔΓ. For a fixed non-empty chain Δ, we derive necessary and sufficient conditions for the existence of non-empty solutions Γ to each of the lexicographic functorial equations (ΔΓ)≤0 ≃ Γ, (Δ Γ)≤0 ≃ Γ and (Δ Γ)≤0 ≃ Γ.

UR - https://www.scopus.com/pages/publications/0141907333

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Functorial equations for lexicographic products

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