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There is a page named "Ordinal analysis" on Wikipedia
- In proof theory, ordinal analysis assigns ordinals (often large countable ordinals) to mathematical theories as a measure of their strength. If theories...51 KB (4,868 words) - 07:44, 25 October 2024
- In statistics, ordinal regression, also called ordinal classification, is a type of regression analysis used for predicting an ordinal variable, i.e....10 KB (1,305 words) - 14:19, 19 September 2024
- Proof theory (section Ordinal analysis)of the major areas of proof theory include structural proof theory, ordinal analysis, provability logic, reverse mathematics, proof mining, automated theorem...19 KB (2,635 words) - 07:52, 18 September 2024
- Other examples of ordinal data include socioeconomic status, military ranks, and letter grades for coursework. Ordinal data analysis requires a different...20 KB (2,706 words) - 02:19, 3 April 2024
- Look up ordinal in Wiktionary, the free dictionary. Ordinal may refer to: Ordinal data, a statistical data type consisting of numerical scores that exist...1 KB (229 words) - 17:42, 14 October 2022
- have computable ordinal notations (see ordinal analysis). However, it is not possible to decide effectively whether a given putative ordinal notation is a...39 KB (5,516 words) - 01:11, 7 November 2024
- definition of ordinal collapsing functions is inextricably intertwined with the theory of ordinal analysis, since the large countable ordinals defined and...68 KB (12,608 words) - 19:13, 16 October 2024
- non-recursive ordinals are large countable ordinals greater than all the recursive ordinals, and therefore can not be expressed using recursive ordinal notations...13 KB (1,815 words) - 07:14, 8 October 2024
in this manner, it is possible to define a cardinal number ℵα for every ordinal number α, as described below. The concept and notation are due to Georg...16 KB (1,957 words) - 08:24, 25 September 2024
the von Neumann ordinal [0]. Then {[0]}, the set whose only element is the empty set, will belong to S2X; this is the von Neumann ordinal [1]. Similarly...18 KB (2,649 words) - 04:29, 23 August 2024- Enumeration (section Ordinals)enumerating function can assume any ordinal. Under this definition, an enumeration of a set S is any surjection from an ordinal α onto S. The more restrictive...11 KB (1,637 words) - 17:00, 15 April 2024
- Ordinal measurement)best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement...38 KB (4,671 words) - 21:41, 23 November 2024
Lane. The Howard ordinal (also known as the Bachmann–Howard ordinal) was named after him. He was the first to carry out an ordinal analysis of the intuitionistic...2 KB (241 words) - 20:28, 23 November 2024 - list Complete theory Independence (from ZFC) Proof of impossibility Ordinal analysis Reverse mathematics Self-verifying theories Model theory Interpretation...11 KB (1,475 words) - 00:52, 5 October 2024
inclusion. The ordinal numbers are a simple example: if each ordinal n is identified with the set [ n ] {\displaystyle [n]} of all ordinals less than or...11 KB (1,725 words) - 04:27, 24 August 2024- Epsilon number (category Ordinal numbers)this ordering (it is in fact the least ordinal with this property, and as such, in proof-theoretic ordinal analysis, is used as a measure of the strength...14 KB (2,106 words) - 11:27, 6 October 2024
- asserting that the ordinal called ε0 is wellfounded; see Gentzen's consistency proof. Gentzen's theorem spurred the development of ordinal analysis in proof theory...92 KB (12,121 words) - 10:12, 29 November 2024
- proof-theoretic ordinal analysis. In ordinal analysis one gauges the strength of theories by measuring how large the (constructive) ordinals are that can...15 KB (1,959 words) - 00:39, 23 June 2024
recursion) an ordinal number α {\displaystyle \alpha } , known as its rank. The rank of a pure set X {\displaystyle X} is defined to be the least ordinal that...42 KB (5,088 words) - 17:30, 4 December 2024- have an ordinal notation in Kleene's O {\displaystyle {\mathcal {O}}} . Arithmetical hierarchy Large countable ordinal Ordinal analysis Ordinal notation...2 KB (229 words) - 22:15, 23 January 2024
- apples and pears? Also in addition to the cardinal numbers there are the ordinal numbers: the fifth apple and the tenth pear claim thought. What is the
- geometrical figures or drawings. "Systems of Logic Based on Ordinals," section 11: The purpose of ordinal logics (1938), published in Proceedings of the London
- Time Series Analysis Multivariate Data Analysis Principal Component Analysis Factor Analysis for metrical data Factor Analysis for ordinal data Canonical