منابع مشابه
Veblen Hierarchy Grzegorz
The Veblen hierarchy is an extension of the construction of epsilon numbers (fixpoints of the exponential map: ω = ). It is a collection φα of the Veblen Functions where φ0(β) = ω and φ1(β) = β . 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 th...
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We study an extension of Japaridze’s polymodal logic GLP with transfinitely many modalities and develop a provability-algebraic ordinal notation system up to the ordinal Γ0. In the papers [1, 2] a new algebraic approach to the traditional prooftheoretic ordinal analysis was presented based on the concept of graded provability algebra. The graded provability algebra of a formal theory T is its L...
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We consider Borel sets of finite rank A C A'" where cardinality of A is less than some uncountable regular cardinal K5. We obtain a "normal form" of A, by finding a Borel set Q, such that A and Q continuously reduce to each other. In more technical terms: we define simple Borel operations which are homomorphic to ordinal sum. to multiplication by a countable ordinal, and to ordinal exponentiati...
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We consider Borel sets of the form A ! (with usual topology) where cardinality of is less than some uncountable regular cardinal. We obtain a \normal form" of A, by nding a Borel set () such that A and () continuously reduce to each other. We do so by deening Borel operations which are homomorphic to the rst Veblen ordinal functions of base required to compute the Wadge degree of the set A: the...
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The aim of this article is to show how Veblen understood and applied Darwinian principles to his analysis of the evolution of socio-economic institutions. At the core of Darwinism is a commitment to causal explanation, which Veblen adopted while not undermining his appreciation of the distinctively purposeful nature of human action. In addition, Veblen applied the Darwinian principles of variat...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2011
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-011-0014-5