Internal set theory (IST) is a mathematical theory of sets developed by Edward Nelson that provides an axiomatic basis for a portion of the nonstandard...

Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any...

particular in model theory and nonstandard analysis, an internal set is a set that is a member of a model. The concept of internal sets is a tool in formulating...

Naive set theory is any of several theories of sets used in the discussion of the foundations of mathematics. Unlike axiomatic set theories, which are...

In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in...

set theory Morse–Kelley set theory Tarski–Grothendieck set theory Ackermann set theory Type theory New Foundations Positive set theory Internal set theory...

nonstandard analysis that he called internal set theory (IST). IST is an extension of Zermelo–Fraenkel set theory (ZF) in that alongside the basic binary...

Look up set theory in Wiktionary, the free dictionary. Set theory is a branch of mathematics concerning mathematical sets. A set theory may also refer...

Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory. The same first-order language...

mathematical logic. In mathematical logic, he was noted especially for his internal set theory, and views on ultrafinitism and the consistency of arithmetic. In...

are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous...

second approach. The extended axioms are IST, which stands either for Internal set theory or for the initials of the three extra axioms: Idealization, Standardization...

graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set S...

they form an ordered field. If formulated in von Neumann–Bernays–Gödel set theory, the surreal numbers are a universal ordered field in the sense that all...

that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics...

enough fragment of arithmetic—including set theories such as Zermelo–Fraenkel set theory (ZF). These set theories cannot prove their own Gödel sentence—provided...

In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements...

It is based on the fact that the set of standard natural numbers N is not an internal subset of the internal set *N of hypernatural numbers. By applying...

the "best fit" linear approximation for a set of points in a domain. Or, it can be used in probability theory to determine the expectation value of a continuous...

studies of graph theory and topology and made influential discoveries in many other branches of mathematics, such as analytic number theory, complex analysis...

the sets that can be defined in a model of a theory, and the relationship of such definable sets to each other. As a separate discipline, model theory goes...

The derivatives and integrals of calculus can be packaged into the modern theory of differential forms, in which the derivative is genuinely a ratio of two...

determinacy Empty set Forcing (mathematics) Fuzzy set Internal set theory Intersection (set theory) L L(R) Large cardinal property Musical set theory Ordinal number...

determinacy Empty set Forcing (mathematics) Fuzzy set Hereditary set Internal set theory Intersection (set theory) Inner model theory Core model Covering...

motivation. Theories of motivation are conceptual frameworks that seek to explain motivational phenomena. Content theories aim to describe which internal factors...

also wrote on the theory of groups and substitutions, the theory of functions, differential equations and determinants. In the theory of light he worked...

example: the complements to the finite sets, it is called the Fréchet filter and it is used in the usual limit theory). If (1) also holds, U is called an...

approach is popular in algebraic geometry. Differentials in smooth models of set theory. This approach is known as synthetic differential geometry or smooth infinitesimal...

part function on the hyperreals. The set ∗ Z {\displaystyle ^{*}\mathbb {Z} } of all hyperintegers is an internal subset of the hyperreal line ∗ R {\displaystyle...

computational complexity theory, decision problems are typically defined as formal languages, and complexity classes are defined as the sets of the formal languages...