In constructive set theory, however, Diaconescu's theorem shows that the axiom of choice implies the law of the excluded middle ( unlike in Martin-Löf type theory, where it does not ).

Some results in constructive set theory use the axiom of countable choice or the axiom of dependent choice, which do not imply the law of the excluded middle in constructive set theory.

then, according to the distributive law, there will be one term in the expansion for each choice of either x or y from each of the binomials of the product.

This is the reason for the frequent choice of the law of the State of New York in commercial contracts.

Commercial contracts almost always include a " choice of law clause " to reduce uncertainty.

) include a Delaware choice of law clause, because of the deep body of law in Delaware on these issues.

Likewise, for litigation of commercial disputes arising out of unpredictable torts ( as opposed to the prospective choice of law clauses in contracts discussed in the previous paragraph ), certain jurisdictions attract an unusually high fraction of cases, because of the predictability afforded by the depth of decided cases.

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.

Although killing oneself is forbidden under normal Jewish law as being a denial of God's goodness in the world, under extreme circumstances when there has seemed no choice but to either be killed or forced to betray their religion, Jews have committed suicide or mass suicide ( see Masada, First French persecution of the Jews, and York Castle for examples ).

Sutherland then released the subsequent companion article in a law journal as part of an academic conference about school choice.

Eusebius said, “ The Creator of all things has impressed a natural law upon the soul of every man, as an assistant and ally in his conduct, pointing out to him the right way by this law ; but, by the free liberty with which he is endowed, making the choice of what is best worthy of praise and acceptance, because he has acted rightly, not by force, but from his own free-will, when he had it in his power to act otherwise, As, again, making him who chooses what is worst, deserving of blame and punishment, as having by his own motion neglected the natural law, and becoming the origin and fountain of wickedness, and misusing himself, not from any extraneous necessity, but from free will and judgment.

* John Coons ( law professor, school choice activist )

Since about 93 % of the data submitted to the FBI is in this format, the UCR stands out as the publication of choice as most states require law enforcement agencies to submit this data.

His choice of a new hometown was somewhat involuntary, taking place whilst he was travelling from Shelbyville, Illinois, to Chicago to find more clients for his law firm.

For advocates of the theory that justice is part of natural law ( e. g., John Locke ), it involves the system of consequences that naturally derives from any action or choice.

The choice principles that intuitionists accept do not imply the law of the excluded middle.

However, in certain axiom systems for constructive set theory, the axiom of choice does imply the law of the excluded middle ( in the presence of other axioms ), as shown by the Diaconescu-Goodman-Myhill theorem.

Although he grew up in a middle class Jewish family, Altenberg eventually separated himself from his family of origin by dropping out of both law and medical school, and embracing Bohemianism as a permanent lifestyle choice.

# Each legal category has one or more choice of law rules to determine which of the competing laws should be applied to each issue.

In those states with an underdeveloped set of Conflict rules, decisions on jurisdiction tend to be made on an ad hoc basis, with such choice of law rules as have been developed embedded into each subject area of private law and tending to favour the application of the lex fori or local law.

In many cases such a selection can be made without invoking the axiom of choice ; this is in particular the case if the number of bins is finite, or if a selection rule is available: a distinguishing property that happens to hold for exactly one object in each bin.

Abd al-Rahman's alleged favorite son was his choice for successor, and would later be known as Hisham I. Abd ar-Rahman's progeny would continue to rule al-Andalus in the name of the house of Umayya for several generations, with the zenith of their power coming during the reign of Abd al-Rahman III.

* Controversy over exact choice of rules for gun safety ( specifically whether or not " the gun is always loaded " is an intelligent rule ).

* Efforts to improve fairness by reducing first-move advantage include the rule of swap, generalizable as " swap -( x, y, z )" and characterizable as a partially compounded and partially iterated version of the pie rule (" one person slices ; the other chooses "): One player places on the board x stones of the first-moving color and a lesser number y stones of the second-moving color (" slicing " in the pie metaphor ); the other player is entitled to choose between a ) playing from the starting position, in which case the selecting player is also entitled to choose which color to play, and b ) placing z ( usually-y ) + 1 ) more stones on the board at locations of that player's choice (" reslicing " in the pie metaphor, with limitations created by the board's existing setup akin to limitations arising from the existing slices in the pie ), in which case the former player is entitled to choose which color side to play.

In Arabic there is no such choice, and the almost invariable rule is that a long vowel is written with a mater lectionis and a short vowel with a diacritic symbol, although the Othmani orthography, the one in which the Qur ' an is traditionally written and printed, has some differences which are not always consistent.

But after the choice was made, he took advantage of the qualities in Eugene III which he objected to, so as to virtually rule in his name.

However, the Court struck down the " choice of expenditure " rule, which required that parties could either make coordinated expenditures for all its candidates, or permit candidates to spend independently, but not both, which they agreed " placed an unconstitutional burden on the parties ' right to make unlimited independent expenditures.

In exchange for Russian support, he agreed to give up any remaining Polish claims to Livonia, and promised to Anna of Russia her choice of successor to the Duchy of Courland, a Polish fief ( of which she had been duchess prior to her ascension to the Russian throne ) which would have otherwise come under direct Polish rule on the death of the current duke, Ferdinand Kettler, who had no heirs.

An n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result for polynomials of degree 2n − 1 or less by a suitable choice of the points x < sub > i </ sub > and weights w < sub > i </ sub > for i = 1 ,..., n.

When it is a player's turn to act, the first verbal declaration or action he takes binds him to his choice of action ; this rule prevents a player from changing his action after seeing how other players react to his initial, verbal action.

In Hellanicus's account, Eteocles offers his brother his choice of either the rule of the city or a share of the property.

In Hellanikos ' account, Eteocles offers his brother his choice of either the rule of the city or a share of the property.

Lê was considered a safe choice because of his time in prison during French rule, his thesis, The Road to the South and his strong belief in Vietnamese reunification.

In 1538 Cromwell deputed Richard Ingworth, Bishop of Dover and former Provincial of the Dominicans, to obtain the friars ' surrender ; which he did by drafting new injunctions that strictly enforced each order's rule, facing the friars with the choice of compliance with the king's wishes, or starvation.

They are radically different, however, in the application of the cooperative principles of freedom of choice and democratic rule.

Thus, some American countries formerly under the Spanish rule have retained the custom of calling it castellano, while others switched to calling it español at some point or the other, with many other different factors influencing the final choice.

The Labour Party had decided not to participate in the election, allowing the electorate to decide on the issue of Home rule versus a Republic by having a clear two way choice between the two nationalist parties.

When the Danish nobility opposed his rule and refused to ratify his choice of Bogislaw IX, Duke of Pomerania as the next King of Denmark, he left Denmark and settled at his castle Visborg in Gotland, apparently a kind of a “ royal strike ” which led to his deposition by the National Councils of Denmark and Sweden in 1439.

However, a recent result seems to rule out such an explanation by showing revaluation of items following a choice even when people have forgotten their choices.

A choice of surface normal allows one to use the right-hand rule to define a " clockwise " direction of loops in the surface, as needed by Stokes ' theorem for instance.

The " analogy of faith ," as a rule of interpretation, he greatly limits, and teaches that it can never afford of itself the explanation, of words, but only determine the choice among their possible meanings.

Chiefs were chosen by the ruling class of the society ; a traditional leader continued to rule not only because he was the choice of what may be termed the nobility, but also because he was accepted by his people.

Therefore those of them who considered a monarchical government as more beneficial to France than a republic, but who were not disposed to hold their freedom subject to the pleasure of one man, became either Bonapartists who professed to rule by the choice of the nation, or supporters of the Orléans princes who were ready to reign by an " original compact " and by the will of the people.