It was logical in its compactness.
A defining feature of any chromosome is its compactness.
Gödel uses compactness to derive a generalization of the completeness theorem.
The printers capable of this are bigger and heavier (though one here, the Epson XP-970, is a miracle of compactness).
This also follows from the compactness theorem, as shown in the entry on classical logic.
As we have seen, the compactness theorem in its usual form fails for all infinitary languages.
However, since the latter is uncountable, the Barwise compactness theorem fails to apply to it.
Many aquatic animals can swim through semisolid mud or muck suspensions, which lack compactness.
The Compactness Theorem would become one of the main tools in the then fledgling subject of model theory.
It may be argued that, by using these principles, the mathematical fictionalist will be entitled to use the compactness theorem.
Whether he loves to read or might appreciate the lightness and compactness of an e-reader, a Kindle is a great gift for recent graduates.
Reykjavik, the far-flung yet surprisingly cosmopolitan capital of Iceland, is filled with more attractions than its compactness might suggest.
We have Soundness and Completeness theorems for classical quantificational logic with identity as well as Compactness and Löwenheim-Skolem theorems.
In that case each finite set of (codes of) L-sentences is also a member of H(ω), and it follows that the compactness theorem for L can be stated in the form:
From then on, the compactness and weight of the massed hoplite phalanx breaking through enemy ranks won battles, not the individual brilliance of aristocratic champions.
. §3 is devoted to a discussion of the compactness problem for infinitary languages and its connection with purely set-theoretical questions concerning “large” cardinal numbers.
Drag is generally considered a negligible influence in terrestrial locomotion; and, in fossorial locomotion, the friction and compactness (friability) of soils are the two major restraints.
In order to establish the conservativeness of mathematics, the mathematical fictionalist has used metalogical results, such as the completeness and the compactness of first-order logic (Field 1992, 1980, 1989).
Also called felting or milling, fulling is a process that increases the thickness and compactness of wool by subjecting it to moisture, heat, friction, and pressure until shrinkage of 10 to 25 percent is achieved.
“must be allowed to be an exception, its Greek derivation being universally admitted, corresponding so exactly as it does in its rectangular form and compactness to the perfection of manhood, according to the views of Plato and Simonides; but any deviation from the simple expression, in which locality is indicated—as, for instance, ‘a genuine Bath’—decidedly breathes the Oriental spirit.”
- the spatial property of being crowded together
- the consistency of a compact solid
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must be allowed to be an exception its Greek derivation being universally admitted corresponding so exactly as it does in its rectangular form and compactness to the perfection of manhood according to the views of Plato and Simonides but any deviation from the simple expression in which locality is indicated—as for instance a genuine Bath—decidedly breathes the Oriental spirit