Sentence examples for choice principle from inspiring English sources

(b) An objection to the choice principle was also put forward by Peano.

(a) The objections to the choice principle were of two kinds.

In (Aczel 1978) the author also considered a choice principle called the Presentation Axiom, which asserts that every set is the surjective image of a so-called base.

These consisted in objections to the choice principle itself, and also objections to the unclarity of the underlying assumptions about, and operation with, sets used in the proof.

In effect, the position is that if one wants to do certain things which, e.g., rely on the WOT, then the choice principle is indispensable.

See also the discussion on choice principles in the main document: Constructive and intuitionistic ZF; there another constructive choice principle, the presentation axiom, is recalled.

Our results, in combination with existing research, essentially complete the classification up to primitive recursive equivalence of those extensions of system T used to give a direct computational interpretation to choice principles.

CZF also included no choice principles.

Accordingly these logical principles may be viewed as choice principles.

Rathjen (2006) has also considered various constructive choice principles and their mutual relations.

A final remark: although constructive and intuitionistic set theories are compatible with the principles of choice just mentioned, the set theories are often defined without any choice principles.