well-ordering

Zermelo introduces axioms of set theory, explicitly formulates AC and uses it to prove the well-ordering theorem, thereby raising a storm of controversy.

The Axiom of Choice Bell, John L. 2008

Zermelo's original purpose in introducing AC was to establish a central principle of Cantor's set theory, namely, that every set admits a well-ordering and so can also be assigned a cardinal number.

The Axiom of Choice Bell, John L. 2008

Contrary to König, Richard did not rely upon the well-ordering of the continuum, and the proposed solution is interesting for the foundational debate to come.

Paradoxes and Contemporary Logic Cantini, Andrea 2007

As for the AC, Gödel exhibits a definable well-ordering, that is, a formula of set theory which defines, in L, a well-ordering of all of L.

Kurt Gödel Kennedy, Juliette 2007

In indirect contexts sense, and not designation, matters and so we may know the well-ordering principle for natural numbers, but not know the principle of mathematical induction because, while they are equivalent in truth value, they have different senses.

Intensional Logic Fitting, Melvin 2007

The need for a specification of infinite sets is crucial in the discussion of the related well-ordering problem.

Paradoxes and Contemporary Logic Cantini, Andrea 2007

One way this could be is if there is no well-ordering of worlds: some worlds are sufficiently different in kind that they are incommensurate with each other (neither is better than the other, nor are they equal).

Free Will O'Connor, Timothy 2005

In the course of development of Cantor's theory of cardinal and ordinal numbers a question was raised whether every set can be provided with a certain structure, called well-ordering of the set.

Set Theory Jech, Thomas 2002

For whatever honour there be in the office of well-ordering a married life, and a family, moved us but slightly.

The Confessions 1999

Then, when in compliance with his mother, and for the well-ordering of the family, he had with stripes corrected those discovered, at her will who had discovered them, she promised the like reward to any who, to please her, should speak ill of her daughter-in-law to her: and none now venturing, they lived together with a remarkable sweetness of mutual kindness.

The Confessions 1999