The representability number of a chain

DOI10.1016/j.topol.2004.05.016zbMath1077.06001OpenAlexW2089224805MaRDI QIDQ1779520

Alfio Giarlotta

Publication date: 1 June 2005

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2004.05.016

zbMATH Keywords

Preference representationAronszajn linesLexicographic orderingRepresentability numberSouslin lines

Mathematics Subject Classification ID

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces (54F05) Utility theory (91B16) Total orders (06A05) Other combinatorial set theory (03E05) Ordered topological structures (06F30)

Related Items (15)

A hierarchy of chains embeddable into the lexicographic power \(({\mathbb{R}}^\omega,\prec_{\text{lex}})\) ⋮ Universal semiorders ⋮ The pseudo-transitivity of preference relations: strict and weak \((m,n)\)-Ferrers properties ⋮ Lexicographic preference representation: intrinsic length of linear orders on infinite sets ⋮ A lattice-theoretical characterization of the family of cut sets of interval-valued fuzzy sets ⋮ The Existence and the Non-existence of Utility Functions in Order-Theoretic, Algebraic and Topological Environments ⋮ The Interplay Between Intergenerational Justice and Mathematical Utility Theory ⋮ On countably saturated linear orders and certain class of countably saturated graphs ⋮ Debreu-like properties of utility representations ⋮ Representable lexicographic products ⋮ Characterizations of standard elements in posets ⋮ Lexicographic preferences representable by real-branching trees with countable height: a dichotomy result. ⋮ A genesis of interval orders and semiorders: transitive NaP-preferences ⋮ Implementations of PACMAN ⋮ Pointwise Debreu lexicographic powers

Cites Work

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• Set theory. An introduction to independence proofs
• Lexicographic behaviour of chains
• A representation for topologically separable chains
• The non-existence of a utility function and the structure of non-representable preference relations
• Representable lexicographic products
• Representations of preference orderings
• Embedding linearly ordered sets in real lexicographic products
• Isomorphisms of Lexicographic Powers of the Reals
• Utility Theory
• $ℵ_0$-categoricity of linear orderings

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