Titlebook: Ordered Sets; Proceedings of the N Ivan Rival Conference proceedings 1982 D. Reidel Publishing Company, Dordrecht, Holland 1982 Lattice.com

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Arithmetic of Ordered Sets and Russell [1912], pp. 291 ff.) When applied to (partially) ordered sets, these operations yield new ordered sets. A unified treatment of these operations was initiated in Birkhoff [1937] and [1942], where it was shown that most of the basic laws of arithmetic apply in this general setting. See al

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Exponentiation and Duality and ., .. (the power) is the set of all order-preserving maps of . (the exponent) to . (the base) ordered componentwise. Our aim. is to review a significant body of results concerning powers of ordered sets and to present some central open problems arising in recent work. Roughly, we have two topic

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Dimension Theory for Ordered Sets intersection of its linear extensions. B. Dushnik and E.W. Miller later defined the . of an ordered set . = 〈.;≤〉 to be the minimum number of linear extensions whose intersection is the ordering ≤..For a cardinal ., . denotes the subsets of ., ordered by inclusion. As the notation indicates, . is a

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Order Types of Real Numbers and Other Uncountable Orderings.. We write ϕ < ψ if ϕ ≤ ψ but it is not the case that ψ ≤ ϕ. The converse type of ϕ is denoted by ϕ *. If . is a class of order types, then a . for . is a set . such that (∀ ψ ∈ .) (∃ ϕ ∈ .) ϕ ≤ ψ..The theory of the class of countable order types is really quite nice. It follows from Ramsey’s Theor

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Infinite Ordered Sets, A Recursive Perspectivecipally concerned with explicit effective constructions, this line of research retains much of the character of the mathematics of finite ordered sets. There are two distinct categories into which the results fall: the first is concerned with individual infinite ordered sets on which the ordering ca

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The Role of Order in Lattice Theoryficant feature of a lattice as an algebraic system is the fact that it has an intrinsic order relation given by.or equivalently..The lattice axioms insure that this relation is a partial order consistent with the lattice operations..The intrinsic character of the lattice ordering sets lattices apart