Hence the pa is an equational formal system, like the many algebraic structures, including Boolean algebra, that are varieties.

Hence the dual algebra has signature 〈 A, ·, +, ', 0, 1, ∀〉, with 〈 A, ·, +, ', 0, 1 〉 a Boolean algebra, as before.

Hence monadic Boolean algebras are the semisimple interior / closure algebras such that:

Hence S5-algebra is a synonym for monadic Boolean algebra.

Hence the construction of pseudorandom generators for the class of Boolean circuits of a given size rests on currently unproven hardness assumptions.

Hence, the only complex Banach algebra which is a division algebra is the complexes.

Hence the following dilemma: Either must be held to be an impossible expression in general, or else the meaning of the fundamental symbol of algebra must be extended so as to include rational fractions.

Hence the Lie algebra of infinitesimal symmetries of the conformal structure is infinite dimensional.

Hence no finite set of finite Heyting algebras can supply all the counterexamples to non-laws of Heyting algebra.

Hence Ω ( X ) is not an arbitrary complete lattice but a complete Heyting algebra ( also called frame or locale-the various names are primarily used to distinguish several categories that have the same class of objects but different morphisms: frame morphisms, locale morphisms and homomorphisms of complete Heyting algebras ).

Hence, Apollo then became a master of the lyre.

Hence the fatalistic strain of the poems, and the earlier settings, foreshadowed responses to the universal bereavement of the First World War and became assimilated into them.

) Hence, it became the name of El Cid's horse.

Hence the group included supporters of Trotskyism, like Judith Merril and others who would have been deemed far left for the era ( Frederik Pohl became a member of the Communist Party in 1936, but later quit in 1939 ).

Hence, after 1919, Hayek's legal name became " Friedrich Hayek ", not " Friedrich von Hayek ".

Hence, the region became a melting pot of cultural and / or social interaction among diverse groups.

Hence, in Roman mythology she was called Proserpina, a name erroneously derived by the Romans from proserpere, " to shoot forth " and as such became an emblematic figure of the Renaissance.

Hence satyrs are most commonly described in Latin literature as having the upper half of a man and the lower half of a goat, with a goat's tail in place of the Greek tradition of horse-tailed satyrs ; therefore, satyrs became nearly identical with fauns.

Hence, in this light, both the chicken and the structure of its egg evolved simultaneously from birds that, while not of the same exact species, gradually became more and more like present-day chickens over time.

Hence the main use became to complement tape releases, usually utilities and niche products like the Tasword word processing software and Trans Express, ( a tape to microdrive copying utility ).

Hence, Tamar became a personification of the heyday of Georgia, a perception that has persisted down to the present time.

Hence the long-standing desire of many colonial administrators to establish a unified structure became feasible.

Hence, Singapore became the only country to become independent against its own will.

Hence, 115 years after the nationalization of the telephone system, France Télécom became a private company.

Hence, these provinces became known as the Spanish Netherlands or Southern Netherlands.

Hence Belton became the Brownlow's sole country home.

Hence, Louis Wolcott became Louis X. Elijah Muhammad then replaced his " X " with the " holy name " Farrakhan, an Arabic name meaning " charmer ".

Hence I have very little doubt, that if the whole genus of humble-bees became extinct or very rare in England, the heartsease and red clover would become very rare, or wholly disappear.

Hence, flat chests became appealing to women, although flappers were the most common to wear such bras.

Hence the word BISHU gradually became Bihu to accommodate linguistic preferences. The other suggestion is that " Bi " means " to ask " and " Hu " means " to give " and so came BIHU.

Hence Yan Liang's siege at Boma across from Liyang became unsupported.

Hence the Scandinavian sense of the name became " port of the chieftain ( s )".

Hence, by 1889, the Romanian state became the owner of all of the lines in the Kingdom of Romania, the railway system having a total length of 1, 377 km.

Hence, beginning in 1958, NASA JPL and the Caltech crew became focused primarily on unmanned flight and shifted away from military applications with a few exceptions.

Hence the rational expectations hypothesis, as applied to the representative household, is unrelated to the presence or absence of rational expectations on the micro level and lacks, in this sense, a microeconomic foundation.

Hence the suggestion that the larger theme is friendship – reinforced by a quotation from the Religio Medici which includes the word ' Enigmas ' – can hardly have any foundation ".

Hence, the foundation of Rev 105 was set, with KREV and WREV soon to come.

Hence they aimed firstly to lay the foundation of administration in a restricted manner with the following basic objectives –

Hence Phraates planned to subjugate parts of Media, and especially the foundation wall of the Haron fortress, which was built on peak nearby.

Hence the myth of " luck " or " good fortune " was seen as closely aligned with the essence of spring itself, the burgeoning of new life, and by extension agriculture, which in all societies is the very foundation of prosperity or " good fortune ".

Hence any application of these concepts to practical problems needs to be performed with care.

Hence, if we compare in a practical situation two accounting results of the same production process we do not know which one is better in terms of production performance.

" Hence this trivial episode was of no practical importance, though it does fix the date at which the Cipher Bureau's interest in the Enigma machine began " manifested, initially, in the entirely legal acquisition of a single commercial-model Enigma.

Hence, words and phrases that refer to general periods in the day were more practical.

Hence, the only way Hogg saw the distinct society clause as having legal effect would be in how to read the rest of the Constitution, although he did not expect that adding a " distinct society " clause would have much practical impact.

Hence, applying the GCRA to limit the bandwidth of variable length packets without access to a fast, hardware multiplier ( as in an FPGA ) may not be practical.

Hence it is not thought practical to define a descriptive naming convention, and all charts are named: