In mathematics, the Veblen functions are a hierarchy of normal functions (continuous strictly increasing functions from ordinals to ordinals), introduced...

Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics...

arithmetic). Many larger epsilon numbers can be defined using the Veblen function. A more general class of epsilon numbers has been identified by John...

2-variable Veblen functions (Veblen 1908) can be used to give a system of ordinal notation for ordinals less than the Feferman-Schutte ordinal. The Veblen functions...

Thorstein Bunde Veblen (/ˈθɔːrstaɪn ˈvɛblən/; July 30, 1857 – August 3, 1929) was an American economist and sociologist who, during his lifetime, emerged...

constructed by Veblen using an extension of Veblen functions allowing infinitely many arguments. Veblen, Oswald (1908), "Continuous Increasing Functions of Finite...

f ′(α) is the α-th fixed point of f. For a hierarchy of normal functions, see Veblen functions. Johnstone 1987, Exercise 6.9, p. 77 Johnstone 1987, Exercise...

factor of 2 in grain diameter. A sentence in first-order logic. The Veblen function in set theory. Porosity in geology and hydrology. Strength (or resistance)...

the Veblen functions to produce countable ordinals even for uncountable arguments, and some of which are "collapsing functions". The small Veblen ordinal...

(1899), by Thorstein Veblen, is a treatise of economics and sociology, and a critique of conspicuous consumption as a function of social class and of...

\varphi _{\gamma }} is called the γ t h {\displaystyle \gamma ^{th}} Veblen function (to the base ω {\displaystyle \omega } ). Ordering: φ α ( β ) < φ γ...

mathematics, the Veblen ordinal is either of two large countable ordinals: The small Veblen ordinal The large Veblen ordinal Veblen function This disambiguation...

modifications of the Veblen functions to produce countable ordinals even for uncountable arguments, and some of which are "collapsing functions". The last one...

starting with 0 and using the operations of ordinal addition and the Veblen functions φα(β). That is, it is the smallest α such that φα(0) = α. This ordinal...

This function was used by Chris Bird, who also invented the next OCF. Chris Bird devised the following shorthand for the extended Veblen function φ {\displaystyle...

including ordinal versions of tetration, pentation, and hexation. See also Veblen function. Every ordinal number α can be uniquely written as ω β 1 c 1 + ω β...

of peak oil). Veblen believed technological developments would eventually lead to a socialistic reorganization of economic affairs. Veblen saw socialism...

econometrics, the Cobb–Douglas production function is a particular functional form of the production function, widely used to represent the technological...

(Levy 1979: p. 117). It was first proved by Oswald Veblen in 1908. A normal function is a class function f {\displaystyle f} from the class Ord of ordinal...

theorem, with the proof-theoretic ordinal of the theorem equaling the small Veblen ordinal (sometimes confused with the smaller Ackermann ordinal). Suppose...

can also be defined as φεΩ+1(0) for an extension of the Veblen functions φα to certain functions α of ordinals; this extension was carried out by Heinz...

φω1(1) (or φω1(2) depending on the notation), where φγ is the γth Veblen function to the base ω1 (instead of the usual ω). As for the Wadge lemma, this...

collapsing functions as defined in their respective citations. Ψ represents either Rathjen's or Stegert's Psi. φ represents Veblen's function. ω represents...

refers to a goal or objective that we wish to maximize, i.e., an objective function. This kind of utility bears a closer resemblance to the original utilitarian...

quantum field theory the probability density function of the normal distribution in statistics the Veblen functions χ {\displaystyle \chi } represents: the...

transformations and convexity" (PDF). Retrieved 27 February 2017. Oswald Veblen (1918) Projective Geometry, volume 2, pp. 105–7. Schneider, Philip K.; Eberly...

constructibility Veblen 1.  Oswald Veblen 2.  The Veblen hierarchy is a family of ordinal valued functions, special cases of which are called Veblen functions. Venn...

inferior items, Veblen goods are generally high quality goods. The demand for Veblen goods increases with the increase in price. Examples of Veblen goods are...

the order types of recursive path orderings with n function symbols is φ(n,0), using Veblen's function for large countable ordinals. The multiset path ordering...

in greater quantity than practical. In 1899, the sociologist Thorstein Veblen coined the term conspicuous consumption to explain the spending of money...