Sentence examples for cardinal notions from inspiring English sources

Much stronger large cardinal notions arise from considering strong reflection properties.

By allowing reflection for more complex second-order, or even higher-order, sentences one obtains large cardinal notions stronger than weak compactness.

Kunen's Theorem opens the door to formulating large cardinal notions stronger than measurability by requiring that $M$ is closer to $V$.

Whether or not it comments on death, what the Second Avenue section of the work does offer is a fascinating deconstruction of daily life, based on John Cage's cardinal notion that there is music in everything.

Another important, and much stronger large cardinal notion is supercompactness.

To formulate the next stronger large-cardinal notion, let us say that a subset $C$ of an infinite cardinal $\kappa$ is closed if every limit of elements of $C$ is also in $C$; and is unbounded if for every $\alpha <\kappa$ there exists $\beta\in C$ greater than $\alpha$.

Among logicians and mathematicians he is in addition famous for his work on set theory, model theory and algebra, which includes results and developments such as the Banach-Tarski paradox, the theorem on the indefinability of truth (see section 2 below), the completeness and decidability of elementary algebra and geometry, and the notions of cardinal, ordinal, relation and cylindric algebras.

Swept up in them are several others, perhaps the most irresistible two being the clumsy Bergetto (James Garnon), an Annabella suitor more attracted to Philotis (Alice Haig), and a corrupt Cardinal (Garnon again), whose notions of justice wouldn't be deemed universal.

This material did not involve the general notion of ordinal and cardinal numbers, not even the general notions of relation and function.

Is the perceived value of things an absolute measurable quantity, as in economists' notion of "cardinal utility," or a relative assessment of the various objects being evaluated, as in economists' notion of "ordinal utility"?

Here we prefer to use the name foundation because in the context of CZF regularity usually refers to a different notion, originating from the classical notion of regular cardinal.