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Many principles that imply the axiom of choice in their general form ( such as " Every vector space has a basis ") become provable in weak subsystems of second-order arithmetic when they are restricted.
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Many and principles
Many of Alcott's educational principles are still used in classrooms today, including " teach by encouragement ", art education, music education, acting exercises, learning through experience, risk-taking in the classroom, tolerance in schools, physical education / recess, and early childhood education.
Many consider him the first true scientific aerial investigator and the first person to understand the underlying principles and forces of flight.
Many philosophies and worldviews have a set of classical elements believed to reflect the simplest essential parts and principles of which anything consists or upon which the constitution and fundamental powers of anything are based.
Many of his principles, therefore, found their way back into the mainstream animation consciousness, and can be seen in films such as The Emperor's New Groove and Lilo & Stitch.
Many data structures use both principles, sometimes combined in non-trivial ways ( as in XOR linking )
Many reformers focused on reforming society by reforming education on more scientific, humanistic, pragmatic or democratic principles.
Many effective therapies have been based on the principles of applied behavior analysis, including pivotal response therapy which is used to treat autism spectrum disorders.
Many of the principles and tenets of hacker ethic contribute to a common goal: the Hands-On Imperative.
Many people who have studied improv have noted that the guiding principles of improv are useful not just on stage but in everyday life.
Many of these scholars accept the general principles of the documentary hypothesis and suggest that the Torah consists of inconsistent texts edited together in a way that calls attention to divergent accounts.
Many relays use an electromagnet to operate a switching mechanism mechanically, but other operating principles are also used.
" Many classical rabbis, especially Maimonides, viewed all such beliefs as a violation of Judaic principles of faith.
Many of the same decisions and principles that apply in other criminal investigations and arrests arise also in civil disobedience cases.
Many early and pre-socialist movements as well as later ones drew principles from the Gospels ( see Christian socialism and the Social Gospel movement ) and against the " values " of profiteering, greed, selfishness and hoarding.
Many critics of Smart Growth point to deficiences in Smart Growth regulations — it is hard to criticize principles that promote " best practices ," " stewardship ," and " quality of life.
Many of the sacred geometry principles of the human body and of ancient architecture have been compiled into the Vitruvian Man drawing by Leonardo Da Vinci, itself based on the much older writings of the roman architect Vitruvius.
Many other people accept some of the basic principles of social justice, such as the idea that all human beings have a basic level of value, but disagree with the elaborate conclusions that may or may not follow from this.
Many of the systems that Lee studied were not to develop his " Personal JKD " but rather was used to gather the " principles " for incorporation in the JKD Framework approach.
Many of Spinoza's ideas continue to vex thinkers today and many of his principles, particularly regarding the emotions, have implications for modern approaches to psychology.
Many and imply
Many coins from Decapolis cities identify their city as " autonomous ," " free ," " sovereign ," or " sacred ," terms that imply some sort of self-governing status.
Many patterns imply object-orientation or more generally mutable state, and so may not be as applicable in functional programming languages, in which data is immutable or treated as such.
Many common beliefs about social organization, such as " Increasing police decreases crime ", or " corruption can be combatted by legislation " imply a first-order mechanism.
Many philosophers, particularly those seeing themselves as within the modern project, use postmodernity to imply the presumed results of holding postmodernist ideas.
Many of the recent Vatican II Council's statements imply that those who do not know the gospel and adhere to other religions can be saved without holding the Catholic faith or religion.
Many Democrats criticized the mailer as misleading, as it could imply that Ehrlich and Steele were Democrats.
Many religious traditions imply the importance of being quiet and still in mind and spirit for transformative and integral spiritual growth to occur.
We might call this kind " human ," if to do so did not imply that 1 and 2 were somehow less than human. In the 1983 edition of The Rhetoric of Fiction, in which a lengthy addendum to the original 1961 book was published, Booth outlined various identities taken on by both authors and readers: The Flesh-and Blood Author, the Implied Author, the Teller of This Tale, the Career Author, and the " Public Myth "; and, the Flesh-and-Blood Re-Creator of Many Stories, the Postulated Reader, the Credulous Listener, the Career Reader, and the Public Myth about the " Reading Public.
Many broadcast shows use stock-footage clips as establishing shots of a particular city, which imply that the show is shot on location when in fact, it may be shot in a Burbank studio.
Many ancient historical accounts from around the world refer to or imply a creation of the earth and universe.
Many researchers believe that these results imply that p73 may not be a tumor suppressor but rather an oncoprotein.
Many and axiom
Many formalists would say that in practice, the axiom systems to be studied will be suggested by the demands of science or other areas of mathematics.
Many earlier results uncover the logical incompatibility of various axioms and, having revealed thus the aggregation problem, suggest reformulation or theoretical triage in dropping some axiom ( s ).
Many and choice
Many theorems which are provable using choice are of an elegant general character: every ideal in a ring is contained in a maximal ideal, every vector space has a basis, and every product of compact spaces is compact.
Many would also find it unacceptable that an ISP, whether by law or by the ISP's own choice, should deploy such software without allowing the users to disable the filtering for their own connections.
Many flame wars have been fought between groups insisting that their editor of choice is the paragon of editing perfection, and insulting the others.
Many castles, especially royal castles were left to decay in the 15th century ; Kenilworth, however, continued to be used as a centre of choice, forming a late medieval " palace fortress ".
Many expected Robinson to be the choice, but the party leader instead picked an unknown, new senior counsel called John Rogers.
Many stations target younger listeners, because advertisers believe that advertising can change a younger person's product choice.
Many contracts and other forms of legally binding agreement include a jurisdiction or arbitration clause specifying the parties ' choice of venue for any litigation ( called a forum selection clause ).
Many opponents of school choice such as Martin Carnoy argue that public schools perform similarly to private schools when teaching similar groups of students, and that the conception of public schools as " failing " in comparison to private schools is more due to the demographic differences between public and private schools than to actual differences in the quality of the education the schools offer.
Many of the Mexican soldiers garrisoned in Tejas were convicted criminals who were given the choice of prison or serving in the army in Tejas.
Many of these conditions can be helped with surgery, and an air conduction hearing aid is often a good choice of treatment.
Many of the new immigrants dropped their traditional customs and laws, both out of choice ( the U. S. offered them a chance to escape what they viewed as the constraints of religious identity ) or not ( Jews refusing to work on the Sabbath were almost always fired at the end of the week ;; the large majority of those who desisted from working on Saturday had to face the formidable challenge of finding new work each week ).
Many schools across South Africa also provide the choice between a summer and winter uniform, with khaki uniforms and brown shoes being very common in the summer.
Many of her ministers were suspicious of the civil service, in light of public choice research that suggested public servants tend to increase their own power and budgets.
" Many voice experts would disagree with this choice of terminology, reserving the designation " head voice " for the high damped register accompanied by a relatively low larynx that is typical of modern high operatic tenor voice production.
Many times, though, the electors are simply important people whose wisdom would ideally provide a better choice than a larger body.
Many commentators were surprised by the choice of Stransky, whom they did not see as a worthy successor to Mahler.
Many Fayetteville residents and farmers sold or donated land for the right of way to influence the choice.
Many of the physical attributes as described in the texts of the Avesta coincide with the choice of plant used in present-day Zoroastrian practice.
Many Christian Scientists use prayer as their first choice for treatment over medicine, including drugs and surgery.
Many historians have suggested that Hillery was Lemass's first choice to succeed him, however others have said that the Lemass pecking order went as follows: Jack Lynch, Hillery and George Colley.