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A logical system which possesses an explicitly stated set of axioms from which theorems can be derived.

A class of processes which attempt to round off a domain and simplify its theory by adjoining elements.

If f_1,...,f_m:R^n->R are exponential polynomials, then {x in R^n:f_1(x)=...f_n(x)=0} has finitely many connected components.

The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.

X subset= R^n is semianalytic if, for all x in R^n, there is an open neighborhood U of x such that X intersection U is a finite Boolean combination of sets {x^_ in ...

X subset= R^n is subanalytic if, for all x in R^n, there is an open set U and a bounded semianalytic set Y subset R^(n+m) such that X intersection U is the projection of Y ...

Arithmetic is the branch of mathematics dealing with integers or, more generally, numerical computation. Arithmetical operations include addition, congruence calculation, ...

In geometry, the term "enlargement" is a synonym for expansion. In nonstandard analysis, let X be a set of urelements, and let V(X) be the superstructure with individuals in ...

Consider an n×n (0, 1)-matrix such as [a_(11) a_(23) ; a_(22) a_(34); a_(21) a_(33) ; a_(32) a_(44); a_(31) a_(43) ; a_(42) a_(54); a_(41) a_(53) ; a_(52) a_(64)] (1) for ...

An ellipse is a curve that is the locus of all points in the plane the sum of whose distances r_1 and r_2 from two fixed points F_1 and F_2 (the foci) separated by a distance ...