There are important statements that, assuming the axioms of ZF but neither AC nor ¬ AC, are equivalent to the axiom of choice.

* statements assuming a combination of intention and probability (" they are moving ") to distinguish the likely series of events and dependencies (" if they can sell their house they might move to Agrestic or if they can't, to Gardendale ") in which the probability that an attempt to do something complex may fail is explicitly acknowledged and not assumed certain.

* statements assuming moral rightness or desirability of a state (" she is happy ") with those that verify the difficulty of determining the state (" she smiles a lot, she seems happy, she would say something if her husband made her angry ", etc.

On the contrary, Marx's statements in his March 1850 Address explicitly contradict such a view, assuming a ' period of petty-bourgeois predominance over the classes which have been overthrown and over the proletariat '.

The following statements refer to the first player, assuming that both players use an optimal strategy.

Moreover, an attempt was made to achieve maximally general statements, while assuming that the reader is aware of the motivations and concrete examples.

Official statements of the EZW are more skeptical, assuming psychological explanations for Lorber's revelations.

The accompanying financial statements have been prepared assuming that the Company will continue as a going concern.

Although Chairperson Born had explained at the October 1, 1998, House Banking Committee hearing that the CFTC ’ s supervisory authority over the LTCM fund as a “ commodity pool operator ” was limited to monitoring its exchange trading activities, the CFTC ’ s possession of financial statements for the fund received negative news coverage in November 1998 based on the fact the CFTC was the only federal regulator to receive such reports directly from LTCM and had not shared the information with other members of the PWG.

On June 6, 2011, Dykstra was arrested and charged with 25 misdemeanor and felony counts of grand theft auto, identity theft, filing false financial statements, and possession of cocaine, ecstasy, and the human growth hormone, Somatropin.

" The article quotes Chicoine: " I have in my possession sworn statements by several persons whom Bishop Schuckardt told personally that he was the Pope.

But since medical-marijuana users in Ann Arbor are very rarely prosecuted, and because the penalty for first-time possession remains a $ 25 civil-infraction fine, both the 2004 ballot measure itself and Oates's subsequent statements on enforcement may prove to be more symbolic than substantive.

* More formal and complex written statements of ownership that permit the easier assumption of shared risk and ownership in companies, and insurance against risk ;

* Increased fungibility, standardization and transferability of statements documenting the ownership of property, which paves the way for structures such as national markets for companies and the easy transportation of property through complex networks of individuals and other entities ;

The CEO and CFO are now required to unequivocally take ownership for their financial statements under Section 302, which was not the case prior to SOX.

The proposed site would have had to be decontaminated, and contradictory statements about the ownership structure of the development were issued.

Full consolidation, as opposed to partial consolidation, results in financial statements that are constructed as if the parent corporation fully owns these partly owned subsidiaries ; except for two line items that do reflect partial ownership of subsidiaries: net income to common shareholders and common equity.

All the other line items in the financial statements assume a fictitious 100 % ownership.

Examples of these types of statements are declarations of ownership, baptisms, inaugurations, and legal sentences.

For a first order predicate calculus, with no (" proper ") axioms, Gödel's completeness theorem states that the theorems ( provable statements ) are exactly the logically valid well-formed formulas, so identifying valid formulas is recursively enumerable: given unbounded resources, any valid formula can eventually be proven.

Euclidean geometry is an axiomatic system, in which all theorems (" true statements ") are derived from a small number of axioms.

The comedy begins when members of the crowd mishear his statements of peace, love and tolerance (" I think he said, ' blessed are the cheese makers '").

In this setting, the rules ( which may include axioms ) can then be used to derive (" infer ") formulæ representing true statements from given formulæ representing true statements.

Often letters feature simple yet absurd statements (" I'm heading off to the pub in a few minutes and wondered if any of your readers fancied joining me for a pint " or " They say size doesn't matter-if that's true, why can't I get these shoes on?

Subsequent sections discuss the basic tenets of logic, self-referring statements, (" typeless ") systems, and even programming.

ICT design and planning drives both the procurement of new ICT solutions through the production of statements of requirement (" SOR ") and invitations to tender (" ITT ") and is responsible for the initiation and management of ICT Programmes for strategic business change.

In addition to scientific theories, the language also included observation sentences (" the sun rises in the east "), definitions, and mathematical statements.

By the 22nd century BC, Ur-Nammu, an ancient Sumerian ruler, formulated the first law code, consisting of casuistic statements (" if ... then ...").

"), or vice-versa, for statements that are questions but also have a clear sense of exclamation or surprise such as: (" Who do you think you are ?!").

A staunch supporter of the Palestinian cause, he has attracted attention with some of his statements on the Israeli-Palestine conflict One of his most controversial act, and possibly only smear on his career, was his support " à titre amical " (" in title of friendship ") for Roger Garaudy in 1996.

The examinee is then asked to draw conclusions from the statements (" What is the maximum number of people who could be present ?").

* ( video ) includes Mary Moorman statements to media on November 22, 1963 (" This video has been removed due to terms of use violation.

In a 1999 study by Gabriel and Gardner, five separate experiments were conducted to demonstrate gender differences in self-concept: a 20 Statement Test evaluating self-construal (" I am ..." statements ), a series of surveys evaluating trait identification, an exercise evaluating selective memory for emotional events, a diary reading paradigm evaluating selective memory, and a survey concerning a situational dilemma evaluating behavioral intention and desire to behave.

From 2005, all European Union listed companies have to prepare their financial statements using the " International Financial Reporting Standards " (" IFRS "), as modified by the EU.

This fallacy may occur when we confuse generalizations (" some ") for categorical statements (" always and everywhere ").

A further regulation is that commands always go down, unaccompanied by statements, and statements always go up, unaccompanied by commands.

Under this kind of pressure, it is not surprising that Wright would make sweeping statements to the newspapers.

The symposium provides an opportunity to confront the self with specific statements which were made at particular times by identifiable communicators who were addressing definite audiences -- and throughout several hundred pages everyone is talking about the same key symbol of identification.

I have said before how difficult it is to make any precise statements with regard to the character of the Greek and Elizabethan public.

Recent statements by the President and Defense Department spokesmen have, to the contrary, assured us that our lead is very great.

A reporter restricted to the competing propaganda statements of both sides in a major labor dispute, for instance, is unable to tell his readers half of what he knows about the causes of the dispute.

One species is restricted to statements which are neither explicit nor precise regarding a particular person, place, time or thing.

While the U. S. Department of Labor has a program of projecting industry and occupational employment trends and publishing current outlook statements, there is little tangible evidence that these projections have been used extensively in local curriculum planning.

While this influence is a complex matter, depending upon personality factors in the individual as well as upon his social-class experience, there probably are some general statements about social-class background and educational policy that can be made with a fair degree of truth.

When the index words or electronic switches are reserved because of actual usage in the statements described above, the position or order of the statements within the program is not important ; ;

A full description of the DIOCS, DTF, and DUF statements is contained in the 7070 Data Processing System Bulletin `` IBM 7070 Input/Output Control System '', form Aj.

It is now harder to assume telepathy as a basis for the statements -- though research still does not know how far afield ESP can range.

It is very important indeed, in the field of extra-sensory perception and its relation to the survival hypothesis, to know whether the statements are actually only those which any intuitive person might venture and an eager sitter attach to himself.

In another approach to the same procedure, the content of the readings is analyzed so as to see how the particular medium is likely to slant her statements.

It is possible to find out in which categories most of her correct statements fall, and where she makes most of her `` hits ''.

It is impossible to get a fair trial when some of the defendants made statements involving themselves and others ''.

There is no justification for systematizing the random statements of Irenaeus about the image of God beyond this, nor for reading into his imprecise usage the later theological distinction between the image of God ( humanity ) and the similitude of God ( immortality ).

An argument of this form is invalid, i. e., the conclusion can be false even when statements 1 and 2 are true.

If the affiant is a party in the case, the affiant's opponent may be successful in having the affidavit admitted as evidence, as statements by a party-opponent are admissible through an exception to the hearsay rule.

It is possible to prove many theorems using neither the axiom of choice nor its negation ; such statements will be true in any model of Zermelo – Fraenkel set theory ( ZF ), regardless of the truth or falsity of the axiom of choice in that particular model.

Similarly, all the statements listed below which require choice or some weaker version thereof for their proof are unprovable in ZF, but since each is provable in ZF plus the axiom of choice, there are models of ZF in which each statement is true.