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Proof theory, also called metamathematics, is the study of mathematics and mathematical reasoning (Hofstadter 1989) in a general and abstract sense itself. Instead of ...

Let U=(U,<··>) be a T2 associative inner product space over the field C of complex numbers with completion H, and assume that U comes with an antilinear involution xi|->xi^* ...

According to most authors (e.g., Kelley 1955, p. 113; McCarty 1967, p. 144; Willard 1970, p. 92) a regular space is a topological space in which every neighborhood of a point ...

In category theory, a tensor category (C, tensor ,I,a,r,l) consists of a category C, an object I of C, a functor tensor :C×C->C, and a natural isomorphism a = a_(UVW):(U ...

A total order (or "totally ordered set," or "linearly ordered set") is a set plus a relation on the set (called a total order) that satisfies the conditions for a partial ...

An urelement contains no elements, belongs to some set, and is not identical with the empty set (Moore 1982, p. 3; Rubin 1967, p. 23). "Ur" is a German prefix which is ...

A finite field is a field with a finite field order (i.e., number of elements), also called a Galois field. The order of a finite field is always a prime or a power of a ...

Probability is the branch of mathematics that studies the possible outcomes of given events together with the outcomes' relative likelihoods and distributions. In common ...

The branch of geometry dealing with the properties and invariants of geometric figures under projection. In older literature, projective geometry is sometimes called "higher ...

A fundamental system of logic based on the concept of a generalized function whose argument is also a function (Schönfinkel 1924). This mathematical discipline was ...