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These axioms differ basically in whether or not they study a TQFT defined on a single fixed n-dimensional Riemannian / Lorentzian spacetime M or a TQFT defined on all n-dimensional spacetimes at once.
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These and axioms
These are equivalent in the sense that, in the presence of other basic axioms of set theory, they imply the axiom of choice and are implied by it.
These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.
These Dianetic " axioms " can be found in Hubbard books such as Scientology 0-8: The Book of Basics and Advanced Procedures and Axioms.
These axioms have been used nearly unchanged in a number of metamathematical investigations, including research into fundamental questions of consistency and completeness of number theory.
These conditions are examples of separation axioms.
These assumptions are the elementary theorems of the particular theory, and can be thought of as the axioms of that field.
These axioms are still in common use to this day.
These conditions are examples of separation axioms and their further strengthenings define completely normal Hausdorff spaces, or T < sub > 5 </ sub > spaces, and perfectly normal Hausdorff spaces, or T < sub > 6 </ sub > spaces.
These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff.
These conditions are examples of separation axioms.
These operations then satisfy all of the axioms for meets, joins, and complements in a Boolean algebra.
These do not provide a resolution to Hilbert's second question, however, because someone who doubts the consistency of Peano arithmetic is unlikely to accept the axioms of set theory ( which is much stronger ) to prove its consistency.
These three axioms are another way of saying that the binary operation is bilinear.
These types are specified by insisting on some further axioms, such as commutativity or associativity of the multiplication operation, which are not required in the broad definition of an algebra.
These basic beliefs cannot, by definition, be proven ( in the logical sense ) within the worldview precisely because they are axioms, and are typically argued from rather than argued for.
These are not a minimal set of axioms but rather the complete set of possible single folds.
These axioms provide semantics by allowing systems to infer additional information based on the data explicitly provided.
These two properties are called Weyl's axioms.
These are essentially the strongest known large cardinal axioms not known to be inconsistent in ZFC ; the axiom for Reinhardt cardinals is stronger, but is not consistent with the axiom of choice.
These conditions are separation axioms that are somewhat stronger than the more familiar Hausdorff axiom T < sub > 2 </ sub >.
These axioms are sound for standard second-order semantics.
These symbols act on certain rules of formation and are developed by inference from a set of axioms.
These expressions are called axioms, in the case of those previously supposed to be true, or theorems, in the case of those derived.
These axioms have been relatively useful for mathematical treatments of Schwarz-type QFTs, although it isn't clear that they capture the whole structure of Witten-type QFTs.
These and differ
These tubes may differ both in the choice of the electron optical system and in the design of the coupling members.
These three differ from each other in the way they treat vowels: abjads have letters for consonants and leave most vowels unexpressed ; abugidas are also consonant-based, but indicate vowels with diacritics to or a systematic graphic modification of the consonants.
These trees differ from the birches ( Betula, the other genus in the family ) in that the female catkins are woody and do not disintegrate at maturity, opening to release the seeds in a similar manner to many conifer cones.
These types of membranes differ in lipid and protein composition.
These processes differ in the means by which chemical reactions are initiated ( e. g., activation process ) and process conditions.
These two mechanisms differ in the stereochemistry of the products.
These differ in having stouter, woodier stems forming taller shrubs, and in the bell-shaped flowers, the petals not being reflexed.
These single-function devices differ from the more familiar general-purpose CPUs in several ways:
These novels differ from the Western tradition in several points as described by van Gulik:
These organizations ' customs and practices differ widely.
These parties belong to all sides of the political spectrum so the reasons for their Euroscepticism may differ, but they all opposed the ratification of the Treaty of Lisbon.
These four schools share most of their rulings, but differ on the particular hadiths they accept as authentic and the weight they give to analogy or reason ( qiyas ) in deciding difficulties.
These differ from one island to another.
These differ in how the weight of the load is attached.
These machines are mechanically similar since all three types use a handle connected to a flywheel by rope, chain, or strap to provide resistance to the user – the types differ only in braking mechanism.
These differ from automatic or switchblade knives in that the blade is not released by means of a button or catch on the handle ; rather, the blade itself is the actuator.
These two polymorphs differ by a " kinking " of bonds ; this change in structure gives β-quartz greater symmetry than α-quartz, and they are thus also called high quartz ( β ) and low quartz ( α ).
These two cells are identical and do not differ in any way from the original parent cell.
These two versions also differ from each other in their readings of numerous words.
These codes and responsa may differ from each other as regards detail ( and reflecting the above differences, on the weight assigned to various issues ).
These forms differ in terms of the relative orientations of the constituent P < sub > 4 </ sub > tetrahedra.
These two styles differ mainly in the way in which they handle quotation marks.
These differ from conventional PLC types as being suitable for use in safety-critical applications for which PLCs have traditionally been supplemented with hard-wired safety relays.
These systems differ in what they measure, what unit of measurement they use, and where the size 0 ( or 1 ) is positioned.
These differ from the normal disfluencies found in all speakers in that stuttering disfluencies may last longer, occur more frequently, and are produced with more effort and strain.
0.738 seconds.