transfinite hierarchy

См. также в других словарях:

• Borel hierarchy — In mathematical logic, the Borel hierarchy is a stratification of the Borel algebra generated by the open subsets of a Polish space; elements of this algebra are called Borel sets. Each Borel set is assigned a unique countable ordinal number… …   Wikipedia

• Jensen hierarchy — In set theory, the Jensen hierarchy or J hierarchy is a modification of Gödel s constructible hierarchy, L, that circumvents certain technical difficulties that exist in the constructible hierarchy. The J Hierarchy figures prominently in fine… …   Wikipedia

• Difference hierarchy — In set theory, the difference hierarchy over a pointclass is a hierarchy of larger pointclasses generated by taking differences of sets. If Γ is a pointclass, then the set of differences in Γ is . In usual notation, this set is denoted by 2 Γ.… …   Wikipedia

• Von Neumann universe — In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted V, is the class of hereditary well founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is… …   Wikipedia

• mathematics, philosophy of — The philosophy of mathematics attempts to explain both the nature of mathematical facts and entities, and the way in which we have our knowledge of both. Modern philosophy of mathematics began with the foundational studies of Cantor, R. Dedekind …   Philosophy dictionary

• set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… …   Universalium

• Large countable ordinal — In the mathematical discipline of set theory, there are many ways of describing specific countable ordinals. The smallest ones can be usefully and non circularly expressed in terms of their Cantor normal forms. Beyond that, many ordinals of… …   Wikipedia

• Georg Cantor — Infobox Scientist name = Georg Ferdinand Ludwig Cantor image width=225px caption = birth date = birth date|1845|3|3 birth place = Saint Petersburg, Russia death date = death date and age|1918|1|6|1845|3|3 death place = Halle, Germany residence =… …   Wikipedia

• Ε₀ — In mathematics, the epsilon numbers are a collection of transfinite numbers whose defining property is that they are fixed points of an exponential map. Consequently, they are not reachable from 0 via a series of applications of the chosen… …   Wikipedia

• Veblen function — In mathematics, the Veblen functions are a hierarchy of functions from ordinals to ordinals, introduced by harvtxt|Veblen|1908. If phi;0 is any continuous strictly increasing function from ordinals to ordinals, then for any non zero ordinal α,… …   Wikipedia

• Reverse mathematics — is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. The method can briefly be described as going backwards from the theorems to the axioms. This contrasts with the ordinary… …   Wikipedia