ABSOLUTENESS - translation to arabic
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ABSOLUTENESS - translation to arabic

IN MATHEMATICAL LOGIC, PROPERTY OF FORMULA THAT HAS THE SAME TRUTH VALUE IN EACH OF SOME CLASS OF STRUCTURES
Shoenfield's absoluteness theorem; Absoluteness (mathematical logic); Absolute Formula; Shoenfield absoluteness theorem; Shoenfield absoluteness

ABSOLUTENESS         
WIKIMEDIA DISAMBIGUATION PAGE
Absolute (record album); Absolute (disambiguation); Absolutes; The absolute; The Absolute; Absolute, The; Absolute (album); Absoluteness

الصفة

باتّ ; بَتِّيّ ; جازم ; حاسِم ; فاصِل ; قاصِل ; قَطْعِيّ ; يَقِين

ABSOLUTE         
WIKIMEDIA DISAMBIGUATION PAGE
Absolute (record album); Absolute (disambiguation); Absolutes; The absolute; The Absolute; Absolute, The; Absolute (album); Absoluteness

الصفة

بَتِّيّ ; حاسِم ; جازم ; جازم ; قَطْعِيّ ; قَطْعِيّ ; فاصِل ; قاصِل ; حاسِم ; بَتِّيّ ; باتّ ; فاصِل ; يَقِين ; يَقِين ; باتّ ; قاصِل

absolute         
WIKIMEDIA DISAMBIGUATION PAGE
Absolute (record album); Absolute (disambiguation); Absolutes; The absolute; The Absolute; Absolute, The; Absolute (album); Absoluteness
ADJ
كامل مطلق ثابت أساسى
N
المطلق، الحقيقة المطلقة

Definition

absoluteness
n.
1.
Despotism, arbitrariness. See absolutism.
2.
Positiveness, reality, actuality, perfection, ideality, supremeness, etc. See absolute.

Wikipedia

Absoluteness

In mathematical logic, a formula is said to be absolute to some class of structures (also called models), if it has the same truth value in each of the members of that class. One can also speak of absoluteness of a formula between two structures, if it is absolute to some class which contains both of them.. Theorems about absoluteness typically establish relationships between the absoluteness of formulas and their syntactic form.

There are two weaker forms of partial absoluteness. If the truth of a formula in each substructure N of a structure M follows from its truth in M, the formula is downward absolute. If the truth of a formula in a structure N implies its truth in each structure M extending N, the formula is upward absolute.

Issues of absoluteness are particularly important in set theory and model theory, fields where multiple structures are considered simultaneously. In model theory, several basic results and definitions are motivated by absoluteness. In set theory, the issue of which properties of sets are absolute is well studied. The Shoenfield absoluteness theorem, due to Joseph Shoenfield (1961), establishes the absoluteness of a large class of formulas between a model of set theory and its constructible universe, with important methodological consequences. The absoluteness of large cardinal axioms is also studied, with positive and negative results known.

Examples of use of ABSOLUTENESS
1. He was possessed of only absoluteness and unconditionality as unswerving faith.
2. Even if statistical absoluteness existed, claim those experts, it is impossible to conclude that there is a causative link between the incidence of a disease and proximity to Ramat Hovav.
3. "This absoluteness I saw in the American president in 2002, not only in our private talks but also in his public comments, reinforced my political skepticism –– even though I personally like America and its president." Germany had sent nearly 4,000 troops to support the U.S.–led war on terrorism in Afghanistan and Africa before that in 2001.