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...ect to some collection of constructive methods. The term "computable real number" has approximately the same meaning. The latter is used in those situation

be a prime number; an $ \ell $-adic sheaf on a scheme $ X $ is said to be constructible (respectively, locally constant) if all sheaves $ F _ {n} $

''Gödel constructible set, constructible set'' ...$ L $ and introduced the following axiom of constructibility: Every set is constructible. On the basis of the axioms of $ \mathsf{ZF} $, he proved that in $ L $, al

* The field of [[constructible number]]s is quadratically closed but not algebraically closed.<ref name=Lam220>La * The quadratic closure of the field of rational numbers is the field of constructible numbers.

A method of defining functions on [[Ordinal number|ordinal numbers]] or, more generally, on sets endowed with an ordinal struc ...important in set theory (e.g., the class of [[Gödel constructive set|Gödel-constructible sets]]) are defined by means of transfinite recursion. The analogy between

...HL), or its negation, which is denoted by (LH), are used in the proof of a number of theorems in general topology. For example, (LH) is equivalent to one of .../TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A. Mostowski, "Constructible sets ands applications" , North-Holland (1969)</TD></TR></table>

...lgebraic equations, while the solution of the inhomogeneous problem is a [[constructible subset]] in the sense of algebraic geometry, i.e. a finite union of sets of ...le set instead of an algebraic set, the problem of projecting an arbitrary constructible set in $P^n$ on the coordinate space of $x_2,\dots,x_n$ must be considered.

...the roots of the general cubic do not lie in the field of [[constructible number]]s. Thus, the problem of trisecting a general angle cannot be solved by mea

...every condition from the system (defining, in general, an infinite set of constructible objects) is represented by a finite approximation of it. The fact that the is put in correspondence, during the construction process, with a natural number, which is a candidate for the role of the element whose inclusion in the se

A formula that expresses the number of fixed points of an endomorphism of a topological space in terms of the t be the [[Lefschetz number|Lefschetz number]] of $ f $.

...ecision problems accepted by Turing machines using at most some polynomial number of steps, $P = \cup _ { k = 1 } ^ { \infty } \operatorname { DTIME } [ n ^ ...that any computation may take on this input, not the exponentially greater number of steps required to simulate all possible computations on that input.

...nates of the point sought can be written as expressions involving a finite number of the operations of addition, multiplication, division, and extraction of ...s the order $2^k$, $k \in \mathbf{N}$. For example, the regular $n$-gon is constructible if and only if each odd prime power dividing $n$ is a [[Fermat prime]] $2^{

be a fixed positive real number and let $ f : {\mathbf R ^ {n} } \rightarrow {\mathbf R ^ {n} } $ ($ n be a fixed real number and let $ f : {\mathbf R ^ {n} } \rightarrow {\mathbf R ^ {n} } $ ($ n

...sification of functions, in so-called Baire function classes, and proved a number of theorems concerning these functions (cf. [[Baire classes|Baire classes]] set with a countable-to-multiple projection is the union of a countable number of uniform $ B $-

...the same idealization one may allow, after having constructed some natural number, the possibility of constructing the next, adding one more stroke to the al ...by using the [[Formalization method|formalization method]] one can find a number of important results on the logic of intuitionism.

...ns without derivatives. The need appeared to separate the notion of a real number from the vague notion of a "variable" , which was based on geometric intui ...nt. For the proof of his result Gödel introduced the important idea of a [[constructible set]] and proved the existence of a model of $ \Sigma $

is some real number, and if ...y extending the sets of strategies (and, therefore, the sets of situations constructible from them). For non-cooperative games, mixed (randomized) strategies are fr