Page "Second-order logic" ¶ 28
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## Some Related Sentences

Soundness and provable
Soundness of a deductive system is the property that any sentence that is provable in that deductive system is also true on all interpretations or structures of the semantic theory for the language upon which that theory is based.

Soundness and is
Soundness is among the most fundamental properties of mathematical logic.
Soundness properties come in two main varieties: weak and strong soundness, of which the former is a restricted form of the latter.
* Soundness: if the statement is false, no prover, even if it doesn't follow the protocol, can convince the honest verifier that it is true, except with some small probability.
* Soundness: if the string is not in the language, no prover, however malicious, will be able to convince the verifier to accept the string with probability exceeding 1 / 3.
# Soundness: if the statement is false, no cheating prover can convince the honest verifier that it is true, except with some small probability.
* Soundness, a logical term meaning that an argument is valid and its premises are true
Soundness guarantees that all possible behaviours are preserved while completeness guarantees that no behaviour is added by the encoding.

Soundness and .
Validity and Soundness in the Internet Encyclopedia of Philosophy.
In Quality of Management they scored second place, third in Long Term Investments, fourth in Financial Soundness, and ninth in Global Competitiveness.
It was established by the Federal Housing Enterprises Financial Safety and Soundness Act of 1992.

Every and provable
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.
* ( Completeness ) Every universally valid second-order formula, under standard semantics, is provable.
* Complete: Every sentence or its negation is a theorem provable from the axioms ;

Every and second-order
For example, second-order arithmetic can express the principle " Every countable vector space has a basis " but it cannot express the principle " Every vector space has a basis ".
Every second-order linear ODE with three regular singular points can be transformed into this equation.
Every second-order linear ODE on the extended complex plane with at most four regular singular points, such as the Lamé equation or the hypergeometric differential equation, can be transformed into this equation by a change of variable.

Every and sentence
Every sentence is a riot.
Every sentence must contain formal words to designate what Husserl calls " formal categories ".
Every sentence typically ends in the trademark elongated tail-off on the last word.
Every open sentence must have ( usually implicitly ) a universe of discourse describing which numbers are under consideration as solutions.
" Every sentence that they write -- every word that they speak -- every resistance that they make, against foreign oppression, is a call upon their slaves to destroy them ," Garrison wrote.
Chekhov wrote The Cherry Orchard during the course of several years, alternating between periods of lighthearted giddiness and despondent frustration which he considered as bordering upon sloth ( in a letter he wrote, " Every sentence I write strikes me as good for nothing.
Every sentence man uses with I, refers to the two pairs: I-Thou and I-It.
Every death sentence involves first an eligibility determination and then a selection of an eligible defendant for the death penalty.
Every sentence has two meanings – one in the novel and one that tells something about Communism.
Every sentence Zansu says ends in " Zansu ".
Every other sentence and punishment is non-custodial, such as fines, judicial beatings, various mandatory but ' open ' therapy and courses, restriction orders, loss or suspension of civil rights, or even suspended sentences.
Every male and female convict sentenced to transportation in Great Britain is sent to Millbank previous to the sentence being executed.

Every and is
Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.
Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.
Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.
Every single problem touched on thus far is related to good marketing planning.
Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.
Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.
Every man in every one of these houses is a Night Rider.
Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Every infinite game in which is a Borel subset of Baire space is determined.
Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).
Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.
Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.
* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =
Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.
Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

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