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Social Choice and Welfare, 2020
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Christopher P. Chambers +1 more
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Christopher P. Chambers +1 more
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Journal of Classification, 2019
The prediction of the values of ordinal response variables using covariate data is a relatively infrequent task in many application areas. Accordingly, ordinal response variables have gained comparably little attention in the literature on statistical prediction modeling.
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The prediction of the values of ordinal response variables using covariate data is a relatively infrequent task in many application areas. Accordingly, ordinal response variables have gained comparably little attention in the literature on statistical prediction modeling.
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Mathematical Structures in Computer Science, 2006
The notion of ordinal computability is defined by generalising standard Turing computability on tapes of length $\omega$ 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 ...
Peter Koepke, Martin Koerwien
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The notion of ordinal computability is defined by generalising standard Turing computability on tapes of length $\omega$ 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 ...
Peter Koepke, Martin Koerwien
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Answering Ordinal Questions with Ordinal Data Using Ordinal Statistics
Multivariate Behavioral Research, 1996It is argued that ordinal statistical methods are often more appropriate than their more common counterparts for three types of reasons: Conclusions from them will be unaffected by monotonic transformation of the variables, they are statistically more robust when used appropriately, and they often correspond more closely to the goals of the ...
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Theories and Ordinals: Ordinal Analysis
2007How do ordinals gauge the strength and computational power of theories and what kind of information can be extracted from this correlation? This will be the guiding question of this talk. The connection between ordinal representation systems and theories is established in ordinal analysis, a central area of proof theory. The origins of proof theory can
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Journal of Symbolic Logic, 1974
We study in this paper the projective ordinals , where = sup{ξ: ξis the length of a Δn1prewellordering of the continuum}. These ordinals were introduced by Moschovakis in [8] to serve as a measure of the “definable length” of the continuum. We prove first in §2 that projective determinacy implies , for all even n > 0 (the same result for odd n is ...
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We study in this paper the projective ordinals , where = sup{ξ: ξis the length of a Δn1prewellordering of the continuum}. These ordinals were introduced by Moschovakis in [8] to serve as a measure of the “definable length” of the continuum. We prove first in §2 that projective determinacy implies , for all even n > 0 (the same result for odd n is ...
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Ordinal Numbers and Ordinal Terms
1977In this chapter we develop a constructive system of ordinals which we shall use in §16 and Chapter VIII for the proof-theoretic treatment of pure number theory and predicative analysis. In §13 we start from a non-constructive presentation of the. classical theory of ordinals in which we take as basis a corresponding axiomatic characterization of the ...
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1989
Abstract In the analysis of categorical data, ordinal variables are commonly encountered. The categories are known to have an order but knowledge of the scale is insufficient to consider them as forming a metric. Although they may be treated simply as nominal categories, as in the first two chapters, valuable information is being lost ...
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Abstract In the analysis of categorical data, ordinal variables are commonly encountered. The categories are known to have an order but knowledge of the scale is insufficient to consider them as forming a metric. Although they may be treated simply as nominal categories, as in the first two chapters, valuable information is being lost ...
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Ordinal Trees and Computable Ordinals
1987In chapter 2.6 we have indicated how appropriate finite path trees can be used for specifying infinite computable production processes. We shall generalize Definition 2.7.5 of trees by also admitting nodes with infinite branching. Such nodes will serve as names for functions with infinitely many arguments such as “\( \mathop {\lim }\limits_{n \to ...
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