منابع مشابه
Using Transfinite Ordinal Conditional Functions
Ordinal Conditional Functions (OCFs) are one of the predominant frameworks to define belief change operators. In his original paper Spohn defines OCFs as functions from the set of worlds to the set of ordinals. But in subsequent paper by Spohn and others, OCFs are just used as functions from the set of worlds to natural numbers (plus eventually +∞). The use of transfinite ordinals in this frame...
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An ordinal-valued metric, taking its values in the set א1 of all countable ordinals, can be assigned to a metrizable set M of nodes in any transfinite graph. M contains all the nonsingleton nodes, as well as certain singleton nodes. Moreover, this yields a graphical realization of Cantor’s countable ordinals, as well as of the Aristotelian ideas of “potential” and “actual” infinities, the forme...
متن کاملThe Transfinite Hausdorff Dimension
Making an extensive use of small transfinite topological dimension trind, we ascribe to every metric space X an ordinal number (or −1 or Ω) tHD(X), and we call it the transfinite Hausdorff dimension of X. This ordinal number shares many common features with Hausdorff dimension. It is monotone with respect to subspaces, it is invariant under bi-Lipschitz maps (but in general not under homeomorph...
متن کاملTransfinite Iteration Functionals and Ordinal Arithmetic
Although transfinite iteration functionals have been used in the past to construct ever-larger initial segments of the ordinals ([5],[1]), there appears to be little investigation into the nature of the functionals themselves. In this note, we investigate the relationship between (countable) transfinite iteration and ordinal arithmetic. While there is a nice connection between finite iteration ...
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Mean value interpolation is a simple, fast, linearly precise method of smoothly interpolating a function given on the boundary of a domain. For planar domains, several properties of the interpolant were established in a recent paper by Dyken and the second author, including: sufficient conditions on the boundary to guarantee interpolation for continuous data; a formula for the normal derivative...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1969
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1969-0240792-0