Sentence examples for wellfounded from inspiring English sources

The answer is that, although it may be a mistake to think that all sets are wellfounded, it is not a mistake to think that the concept of wellfounded set is worth axiomatising.

If Hilbert's worry is wellfounded in the sense that there are no concrete physical systems that make the postulates of mathematical analysis true, then the above nominalist structuralist rendering of the content of a sentence φ of the language of analysis gets the truth conditions of such sentences wrong.

A set x is wellfounded if there are no infinite sequences …xn ∈ xn-1 ∈ …x3 ∈ x2 ∈ x1.

Indeed as far as we know we can safely add to NF some axioms to say that the wellfounded sets form a model of ZFC.

This project has been so successful that nowadays many people believe that wellfounded sets are the only kind of set there is if it isn't wellfounded it isn't a set but a hyperset perhaps.

The fact that NF refutes the axiom of choice sharpens the consistency problem greatly, and ought to sharpen public interest, but the widely-held view that sets are, of their essence, wellfounded represents a huge rhetorical obstacle to NF attracting the attention that its foundational interest merits.

"I find it strange that DfID are relying on consultants rather than making these decisions themselves," says Dave Pearce, chief operating officer at Operation Wellfound, a British charity that has just had an application for funding to build wells and latrines for disadvantaged communities in Burkina Faso refused for a second time.

There are obviously structural differences between the ordinary paradoxes of self-reference and Yablo's paradox: The ordinary paradoxes of self-reference involve a cyclic structure of reference, whereas Yablo's paradox involve an acyclic, but non-wellfounded, structure of reference.

Visser (1989) has studied non-wellfounded hierarchies of languages and axiomatizations thereof.

For example, corresponding to the picture in (9) we would take X = {x0, y0, z0, x1, y1, z1, x2, y2, z2, x3, y3, z3} The study of non-wellfounded sets proposes to treat every graph as a picture of a unique set.

With AFA, the greatest fixed points usually have non-wellfounded members.