Displaying similar documents to “Characteristics of orders based on choice function tool.”

On rigid relation principles in set theory without the axiom of choice

Paul Howard, Eleftherios Tachtsis (2016)

Fundamenta Mathematicae

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We study the deductive strength of the following statements: 𝖱𝖱: every set has a rigid binary relation, 𝖧𝖱𝖱: every set has a hereditarily rigid binary relation, 𝖲𝖱𝖱: every set has a strongly rigid binary relation, in set theory without the Axiom of Choice. 𝖱𝖱 was recently formulated by J. D. Hamkins and J. Palumbo, and 𝖲𝖱𝖱 is a classical (non-trivial) 𝖹𝖥𝖢-result by P. Vopěnka, A. Pultr and Z. Hedrlín. ...

Binary and ternary relations

Vítězslav Novák, Miroslav Novotný (1992)

Mathematica Bohemica

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Two operators are constructed which make it possible to transform ternary relations into binary relations defined on binary relations and vice versa. A possible graphical representation of ternary relations is described.

Basic Operations on Preordered Coherent Spaces

Klaus Grue, Artur Korniłowicz (2007)

Formalized Mathematics

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This Mizar paper presents the definition of a "Preordered Coherent Space" (PCS). Furthermore, the paper defines a number of operations on PCS's and states and proves a number of elementary lemmas about these operations. PCS's have many useful properties which could qualify them for mathematical study in their own right. PCS's were invented, however, to construct Scott domains, to solve domain equations, and to construct models of various versions of lambda calculus.For more on PCS's,...