QUESTIONS Does the PEDro scale measure only one construct ie, the methodological quality of clinical trials? What is the hierarchy of items of the PEDro scale from least to most adhered to? Is there any effect of year of publication of trials on item adherence? Are PEDro scale ordinal scores equivalent to interval data? DESIGN Rasch analysis of two independent samples of 100 clinical trials f...

The notion of ordinal computability is defined by generalising standard Turing computability on tapes of length ω to computations on tapes of arbitrary ordinal length. The fundamental theorem on ordinal computability states that a set x of ordinals is ordinal computable from ordinal parameters if and only if x is an element of the constructible universe L. In this paper we present a new proof o...

A method is proposed for classification to ordinal categories by applying the search partition analysis (SPAN) approach. It is suggested that SPAN be repeatedly applied to binary outcomes formed by collapsing adjacent categories of the ordinal scale. By a simple device, whereby successive binary partitions are constrained to be nested, a partition for classification to the ordinal states is obt...

We discuss the problem of ranking instances where an instance is associated with an integer from 1 to k. In other words, the specialization of the general multi-class learning problem when there exists an ordering among the instances — a problem known as “ordinal regression” or “ranking learning”. This problem arises in various settings both in visual recognition and other information retrieval...

Let us observe that there exists an ordinal number which is non empty and natural. Let a be a natural ordinal number. Note that succa is natural. The scheme Omega Ind concerns a unary predicate P , and states that: For every natural ordinal number a holds P [a] provided the following conditions are met: • P [ / 0], and • For every natural ordinal number a such that P [a] holds P [succa]. Let a,...

We define a functional interpretation of KPω using Howard’s primitive recursive tree functionals of finite type and associated terms. We prove that the Σ-ordinal of KPω is the least ordinal not given by a closed term of the ground type of the trees (the Bachmann-Howard ordinal). We also extend KPω to a second-order theory with ∆1-comprehension and strict-Π 1 1 reflection and show that the Σ-ord...

We study mechanism which operate on ordinal preference information (i.e., rank ordered lists of alternatives) on the full domain of weak preferences that admits indifferences. We present a novel decomposition of strategyproofness into three axioms: separation monotonic, separation upper invariant, and separation lower invariant. Each axiom is a natural restriction on how mechanisms can react wh...

We show that that if every real has a sharp and there are 1 2-deenable prewellorderings of R of ordinal ranks unbounded in ! 2 , then there is an inner model for a strong cardinal. Similarly, assuming the same sharps, the Core Model K is 1 3-absolute unless there is an inner model for a strong cardinal.