Enderton gives the following characteristics of a procedure for computing a computable function ; similar characterizations have been given by Turing, Rogers, and others.

Enderton goes on to list several clarifications of these requirements of the procedure for a computable function:

The decidability of Presburger arithmetic can be shown using quantifier elimination, supplemented by reasoning about arithmetical congruence ( Enderton 2001, p. 188 ).

* Herbert B. Enderton, Second-order and Higher-order Logic in Stanford Encyclopedia of Philosophy, published Dec 20, 2007 ; substantive revision Mar 4, 2009.

Indeed, the proof that a logical system or theory is undecidable will use the formal definition of computability to show that an appropriate set is not a decidable set, and then invoke Church's thesis to show that the theory or logical system is not decidable by any effective method ( Enderton 2001, pp. 206ff.

He attended Santa Monica High School in the 1970s, where he was a member of the nonmusical group " The Olive Starlight Orchestra ," along with David Linden, Keith Goldfarb, David Coons, Sandra Tsing Loh, Susan P. Crawford, Eric Enderton, and Jan Steckel.

( Kunen 1980 p. 141 ; Enderton 2001 p. 152 ; Burgess 1977 p. 406 ).

Nevertheless, it may be helpful to cite one example -- that of employment -- for, as will be shown below, it cuts across both facets of the new concept.

The promenade, for example, continues to take place on the Chahar Bagh, a mile-long garden of plane and poplar trees that now serves as the city's principal street.

for example, the mode of bravery to this anonymous folk poem: `` They brought me news that Spring is in the plains And Ahmad's blood the crimson tulip stains ; ;

Incapable of self-delusion, the Founding Fathers found the crisis of their time to be equally grave, and yet they had confidence that America would surmount it and that a republic of free peoples would prosper and serve as an example to a world aching for liberty.

An example of the changes which have crept over the Southern region may be seen in the Southern Negro's quest for a position in the white-dominated society, a problem that has been reflected in regional fiction especially since 1865.

The sequence may involve a sharp contrast: for example, a quiet meditative sway of the body succeeded by a violent leap ; ;

This almost trivial example is nevertheless suggestive, for there are some elements in common between the antique fear that the days would get shorter and shorter and our present fear of war.

In agriculture, for example, despite the advances in biology, elaborate rituals tend to persist along with a continued sense of the imminence of some natural disaster.

The creative urge, for example, transcends the body and the self.

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

His name is Praisegod Piepsam, and he is rather fully described as to his clothing and physiognomy in a way which relates him to a sinister type in the author's repertory -- he is a forerunner of those enigmatic strangers in `` Death In Venice '', for example, who represent some combination of cadaver, exotic, and psychopomp.

It resembles, too, pictures such as Durer and Bruegel did, in which all that looks at first to be solely pictorial proves on inspection to be also literary, the representation of a proverb, for example, or a deadly sin.

How did it happen, for example, that the state university, that great symbol of American democracy, failed to flourish in New England as it did in other parts of the country??

This is an unsolved problem which probably has never been seriously investigated, although one frequently hears the comment that we have insufficient specialists of the kind who can compete with the Germans or Swiss, for example, in precision machinery and mathematics, or the Finns in geochemistry.

He and also Mr. Cowley and Mr. Warren have fallen to the temptation which besets many of us to read into our authors -- Nathaniel Hawthorne, for example, and Herman Melville -- protests against modernism, material progress, and science which are genuine protests of our own but may not have been theirs.

Why, for example, should the ancients have supposed the diurnal rotation of the heavens to be elliptical??

A lady, you made clear to me both by precept and example, never raised her voice or slumped in her chair, never failed in social tact ( in heaven, for instance, would not mention St. John the Baptist's head ), never pouted or withdrew or scandalized in company, never reminded others of her physical presence by unseemly sound or gesture, never indulged in public scenes or private confidences, never spoke of money save in terms of alleviating suffering, never gossiped or maligned, never stressed but always minimized the hopelessness of anything from sin to death itself.

In the calm which follows the reading of a poem, for example, is the effect produced by the enforced quiet, by the musical quality of words and rhythm, by the sentiments or sense of the poem, by the associations with earlier readings, if it is familiar, by the boost to the self-esteem for the semi-literate, by the diversion of attention, by the sense of security in a legitimized withdrawal, by a kind license for some variety of fantasy life regarded as forbidden, or by half-conscious ideas about the magical power of words??

In `` My Song's Young Virgin Date '', for example, Thompson wrote: `` Yea, she that had my song's young virgin date Not now, alas, that noble singular she, I nobler hold, though marred from her once state, Than others in their best integrity.

Reviewing Davidson's The Testament Of An Empire Builder, for example, Thompson found that there was `` too much metrical dialectic ''.

In his book Civilization And Ethics Albert Schweitzer faces the moral problems which arise when moral law is recognized in business life, for example.

Those who wanted to close the theaters, for example, pointed to Plato's Republic and those who wished to keep them open called on the Plato of the Ion to testify in their behalf.

In archaeology, for example, the contributions of Frederick Haverfield and Reginald Smith to the various volumes of the Victoria County Histories raised the discipline from the status of an antiquarian pastime to that of the most valuable single tool of the early English historian.

The men around him, observes the narrator, `` have been living from day to day for thousands of years ''.

Orlick shakes his hand at Pip, bangs the table with his fist, draws his unclenched hand `` across his mouth as if his mouth watered '' for his victim, lets his hands hang `` loose and heavy at his sides '', and Pip observes him so intensely that he knows `` of the slightest action of his fingers ''.

Paul Roche observes that the author abounded in mistakes and anachronisms, using Daniel as a symbol for the faithful Jew serving Yahweh, and the use of various pagan kings as symbols of heathenism.

: The claim that EPR effects violate the principle that information cannot travel faster than the speed of light have been countered by noting that they cannot be used for signaling because neither observer can control, or predetermine, what he observes, and therefore cannot manipulate what the other observer measures.

" That is a standard technique in attempting to destabilize and overthrow a government, is to demonstrate to the citizens that it's government cannot provide security for them ," observes David MacMichael, a former CIA analyst on Nicaragua.

Although a steadfast proponent of a radical and rational autonomy in all things, Husserl could also speak " about his vocation and even about his mission under God's will to find new ways for philosophy and science ," observes Spiegelberg.

For example, a thermometer will not display different temperatures for each individual who observes it.

In Western Christianity it has traditionally been taught, since as far back as the time of the Donatist controversy of the fourth and fifth centuries, that any bishop can consecrate any other baptised man as a bishop provided that the bishop observes the minimum requirements for the sacramental validity of the ceremony.

Historian Ian Kershaw observes that many Nazis seemed to have a " psychological block " at the end of the regime, refusing to recognise their responsibility for the barbaric actions that occurred during the Third Reich.

Sorita d ' Este observes that it is also important to give consideration to the difference between the modern calendar and the lunisolar calendars which would have been in use when these dates were set, giving us a full moon date around the 13th of each month and the date for the August festival originating with the festival of Nemoralia held in honour of Diana.

If one carefully observes the third equation one will notice it also works for n

" Calls for reparation, coming many years after the displacement of these people from the land of their ancestors, have not yielded any significant benefits ," observes Basilwizi in its recent report.

The intensity of debate spurred Catholic Church interventions against " heresy " and even a general confiscation of Rabbinic texts and in reaction, the defeat of the more radical interpretations of Maimonides and at least amongst Ashkenazi Jews, a tendency not so much to repudiate as simply to ignore the specifically philosophical writings and to stress instead the Rabbinic and halachic writings ; even these writings often included considerable philosophical chapters or discussions in support of halachic observance, as David Hartman observes Maimonides made clear " the traditional support for a philosophical understanding of God both in the Aggadah of Talmud and in the behavior of the hasid pious Jew " and so Maimonidean thought continues to influence traditionally observant Jews.

Ideas of reflection and the workings of imagination are blended in the term merencolie, embodying for contemporaries " a tendency ", observes Huizinga, " to identify all serious occupation of the mind with sadness ".

Egyptologist Erik Hornung observes that Egyptian Christians continued to mummify corpses ( an integral part of the Osirian beliefs ) until it finally came to an end with the arrival of Islam, and argues for an association between the passion of Jesus and Osirian traditions, particularly in the apocryphal gospel of Nicodemus and Christ's descent into Hades.

W. Paul Adams observes that republic is most often used in the United States as a synonym for state or government, but with more positive connotations than either of those terms.

They are not directly listed in the Torah ; elsewhere, the Mishnah observes that " the laws of Shabbat [...] are like mountains hanging by a hair, for they are little Scripture but many laws ".

It is possible, however, that Stephen had already begun to consider passing over Eustace's claim ; historian Edmund King observes that Eustace's claim to the throne was not mentioned in the discussions at Wallingford, for example, and this may have added to Stephen's son's anger.

He observes, " In the early Church, it seems, the new covenant presented by the New Testament was either taken to be an addition to the old covenant ( the religion of the Torah and the Jewish Pharisaic tradition, summarized in the Ten Commandments ), or it was taken to be a replacement for the old covenant.

She also observes that the chess pieces have come to life, though they remain small enough for her to pick up.

* John Bevis observes the Crab Nebula for the first time.

Neither prospect appealed to Arion: as Robin Lane Fox observes, " No Greek would swim out into the deep from a boat for pleasure.

Although planets can sometimes be mistaken for stars as one observes the night sky, the planets actually change position from night to night in relation to the stars.