Displaying similar documents to “On rigid relation principles in set theory without the axiom of choice”

Definitions of finiteness based on order properties

Omar De la Cruz, Damir D. Dzhafarov, Eric J. Hall (2006)

Fundamenta Mathematicae

Similarity:

A definition of finiteness is a set-theoretical property of a set that, if the Axiom of Choice (AC) is assumed, is equivalent to stating that the set is finite; several such definitions have been studied over the years. In this article we introduce a framework for generating definitions of finiteness in a systematical way: basic definitions are obtained from properties of certain classes of binary relations, and further definitions are obtained from the basic ones by closing them...

Compositions of ternary relations

Norelhouda Bakri, Lemnaouar Zedam, Bernard De Baets (2021)

Kybernetika

Similarity:

In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introduced by Zedam et al. We study the properties of these compositions, in particular the link with the usual composition of binary relations through the use of the operations of projection and cylindrical extension.

Binary and ternary relations

Vítězslav Novák, Miroslav Novotný (1992)

Mathematica Bohemica

Similarity:

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

Similarity:

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,...