In the mathematical field of set theory, ordinal arithmetic describes the three usual operations on ordinal numbers: addition, multiplication, and exponentiation...
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In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite...
48 KB (6,719 words) - 07:54, 17 October 2024
an ordinal number α is the smallest ordinal number greater than α. An ordinal number that is a successor is called a successor ordinal. The ordinals 1...
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interpret a sufficient portion of arithmetic to make statements about ordinal notations. The proof-theoretic ordinal of such a theory T {\displaystyle...
51 KB (4,868 words) - 00:15, 14 October 2024
Cardinal number (redirect from Cardinal arithmetic)
a finite set is the common ordinal number of all possible well-orderings of that set, and cardinal and ordinal arithmetic (addition, multiplication, power...
26 KB (3,808 words) - 01:08, 27 April 2024
the focus on countable ordinals, ordinal arithmetic is used throughout, except where otherwise noted. The ordinals described here are not as large as...
39 KB (5,516 words) - 19:34, 16 October 2024
Epsilon number (category Ordinal numbers)
numbers were introduced by Georg Cantor in the context of ordinal arithmetic; they are the ordinal numbers ε that satisfy the equation ε = ω ε , {\displaystyle...
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counterexamples in topology. Epsilon numbers (mathematics) Large countable ordinal Ordinal arithmetic "Set Theory > Basic Set Theory (Stanford Encyclopedia of Philosophy)"...
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limit ordinal is an ordinal number that is neither zero nor a successor ordinal. Alternatively, an ordinal λ is a limit ordinal if there is an ordinal less...
8 KB (1,083 words) - 20:34, 11 March 2024
the proof-theoretic ordinal of Peano arithmetic. PRA's proof theoretic ordinal is ωω, where ω is the smallest transfinite ordinal. PRA is sometimes called...
9 KB (1,316 words) - 12:53, 21 February 2024