The objective of this paper is to introduce an ordinal representation system which has been employed in the determination of the proof{theoretic strength of 1 2 comprehension and related systems.

We show that in the presence of large cardinals proper forcings do not change the theory of L(R) with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model.

A well known argument of James yields that if a Banach space X contains `1 ’s uniformly, then X contains `1 ’s almost isometrically. In the first half of the paper we extend this idea to the ordinal `1-indices of Bourgain. In the second half we use our results to calculate the `1-index of certain Banach spaces. Furthermore we show that the `1-index of a separable Banach space not containing `1 ...

This paper evaluates the human resource information systems provided by different vendors using two new hybrid multicriteria decision-making methods that require ordinal data as inputs. First, grey-point-allocation full-consistency (Grey-PA-FUCOM) weighting method is proposed. The Grey-PA-FUCOM combines simple point-allocation widely used managers and advanced FUCOM accepted scholars in grey sy...

Abstract The concept of a sectionally pseudocomplemented lattice was introduced in Birkhoff (1979) as an extension relative pseudocomplementation for not necessarily distributive lattices. typical example such is the non-modular N 5 . aim this paper to extend sectional from lattices posets. At first we show that class forms variety which can be described by two simple identities. This has nice ...

Rubinstein, Safra and Thomson (1992) introduced the Ordinal Nash Bargaining Solution. They prove that Pareto optimality, ordinal invariance, ordinal symmetry, and IIA characterize this solution. A feature of their work is that attention is restricted to a domain of social choice problems with an infinite set of basic allocations. We introduce an alternative approach to solving finite social cho...

Background. Historically, most acute stroke clinical trials were neutral statistically, with trials typically dichotomising ordinal scales, such as the modified Rankin Scale. Studies published before 2007 have shown that preserving the ordinal nature of these scales increased statistical power. A systematic review of trials published since 2007 was conducted to reevaluate statistical methods us...

‎‎in this paper‎, ‎we define fuzzy subnexuses over a nexus $n$‎. ‎define and study the notions of the prime fuzzy subnexuses and the fractions‎‎induced by them‎. ‎finally‎, ‎we show that if s is a meet‎‎closed subset of the set fsub(n), ‎of fuzzy subnexuses of a nexus n‎, ‎and‎‎h= ⋀s ϵ s, ‎then the fractions s^-1 n and h^-1 n are isomorphic as meet-semilattices‎.

We define the notion of ordinal computability by generalizing standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. We show that a set of ordinals is ordinal computable from a finite set of ordinal parameters if and only if it is an element of Gödel’s constructible universe L. This characterization can be used to prove the generalized continuum...