An application of higher order fixed points of normal functions.

Šobot, Boris

Displaying similar documents to “An application of higher order fixed points of normal functions.”

Veblen Hierarchy

Grzegorz Bancerek (2011)

Formalized Mathematics

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The Veblen hierarchy is an extension of the construction of epsilon numbers (fixpoints of the exponential map: ωε = ε). It is a collection φα of the Veblen Functions where φ0(β) = ωβ and φ1(β) = εβ. The sequence of fixpoints of φ1 function form φ2, etc. For a limit non empty ordinal λ the function φλ is the sequence of common fixpoints of all functions φα where α < λ.The Mizar formalization of the concept cannot be done directly as the Veblen functions are classes (not (small) sets)....

Compact-like properties in hyperspaces

J. Angoa, Y. F. Ortiz-Castillo, Á. Tamariz-Mascarúa (2013)

Matematički Vesnik

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Non-expansive mappings in spaces of continuous functions.

Tomás Domínguez Benavides, María A. Japón Pineda (2004)

Extracta Mathematicae

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Rectangular axioms, perfect set properties and decomposition

J. Brendle, P. Larson, S. Todorčević (2008)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

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Epsilon Numbers and Cantor Normal Form

Grzegorz Bancerek (2009)

Formalized Mathematics

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An epsilon number is a transfinite number which is a fixed point of an exponential map: ωϵ = ϵ. The formalization of the concept is done with use of the tetration of ordinals (Knuth's arrow notation, ↑). Namely, the ordinal indexing of epsilon numbers is defined as follows: [...] and for limit ordinal λ: [...] Tetration stabilizes at ω: [...] Every ordinal number α can be uniquely written as [...] where κ is a natural number, n1, n2, …, nk are positive integers, and β1 > β2 > …...

On what I do not understand (and have something to say): Part I

Saharon Shelah (2000)

Fundamenta Mathematicae

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This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems are presented with a discussion of how I have tried to solve them, and sometimes with failed tries, anecdotes and opinions. So the discussion is quite personal, in other words, egocentric and somewhat accidental. As we discuss many problems, history...