Sentence examples for constructive notion from inspiring English sources

The claim is that a clear constructive meaning is thus assigned to CZF's notion of set by looking at its meaning in Martin-Löf type theory, since the latter is usually considered as representing an accurate and fully motivated formulation of a constructive notion of set.

But taking the essential versus constructive notions of what it means to be a mother, are egg donors going to feel differently than sperm donors?

For further applications of Kripke models to separating crucial constructive notions, see e.g. (Diener and Lubarsky 2013).

Biggs (2003) articulated these ideas according to the constructive alignment notion; i.e. aligning teaching and assessment to curriculum objectives.

As is often the case in constructive mathematics, very simple notions of classical mathematics (such as the notion of an ordinal) become much more complicated in the constructive environment.

This example shows that in constructive set theory the notion of ordinal does not play the same central role as in classical set theory.

The next step is to choose a good stock of set-theoretic principles which faithfully represent the desired notion of constructive set.

(For the notion of constructive ordinal and a brief discussion of its properties, see the supplementary document on: Set-theoretic Principles Incompatible with Intuitionistic Logic).

The constructive justification of these notions relies again on the type theoretic interpretation.

Variations of the basic notions are especially useful for establishing relative consistency and relative independence of the nonlogical axioms in theories based on intuitionistic logic; some examples are Moschovakis [1971], Lifschitz [1979], and the realizability notions for constructive and intuitionistic set theories developed by Rathjen [2006, 2012] and Chen [2012].

Dora who objected to non-constructive existence proofs could not plausibly be interpreted as just expressing a preference for constructive methods: she found the notion of non-constructive existence unintelligible not just unappealing.