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Wondering how to use Provability in a sentence? Below are 10+ example sentences from authentic English texts. Including the meaning .

Rare word

Provability in a sentence

Provability meaning

The condition of being provable

Synonyms of Provability

demonstrability indisputability indubitability unquestionability unquestionableness

Related words

Other words often associated with Provability or its synonyms:

certainty

Using Provability

  • The main meaning on this page is: The condition of being provable
  • Useful related words include: demonstrability, indisputability, indubitability, unquestionability.
  • In the example corpus, provability often appears in combinations such as: the provability, provability of, provability in.

Context around Provability

  • Average sentence length in these examples: 28 words
  • Position in the sentence: 7 start, 1 middle, 5 end
  • Sentence types: 13 statements, 0 questions, 0 exclamations

Often before:

formal 1× actual 1× non 1×

Often after:

predicate 1× formula 1× itself 1×

Sentence patterns with Provability

These short patterns come directly from the example sentences and show how the word is often embedded:

about the provability of statements 2× about formal provability within these 1× concept of provability and thus 1× denote the provability formula just 1× depend on provability of these 1× notion of provability itself can 1× of their provability 1× own non provability does not 1×

Sentence openings and endings

Common sentence openings:

questions about the 2× also it makes 1× crucially because the 1× in the course 1× provability and theoremhood 1× rather than depend 1×

Common sentence endings:

it were complete 2× a proof system 1× an informal sense 1× been objectively falsified 1× can be defined 1× formula just described 1×

Words around Provability

Just before it in the word index:

prova 2 prov 9 prouvost 2 prouty 10 prout 11 proustian 2

Just after it in the word index:

provable 70 provably 24 provan 10 prove 4.518 proved 5.075 provedel 2

Similar in corpus frequency:

aanand 16 abcd 16 abdurrahman 16 aberdour 16 abergele 16 abg 16

Corpus analysis for Provability

  • In this selection, "provability" usually appears near the start of the sentence. The average example has 28 words, and this corpus slice is mostly made up of statements.
  • Around the word, formal, actual, non, predicate, formula and itself stand out and add context to how "provability" is used.
  • Recognizable usage signals include about the provability of statements and about formal provability within these. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "provability" sits close to words such as aanand, abcd and abdurrahman, which helps place it inside the broader word index.

Example types with provability

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

The incompleteness theorems are about formal provability within these systems, rather than about "provability" in an informal sense. (18 words)

Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified. (20 words)

The relationship between provability in classical (or nonconstructive) systems and provability in intuitionistic (or constructive, respectively) systems is of particular interest. (21 words)

Longer example sentences

They are particularly concerned with the interpretation of a Gödel sentence for an ω-inconsistent system as actually saying "I am not provable", since the system has no models in which the provability predicate corresponds to actual provability. (38 words)

Provability and theoremhood To establish a mathematical statement as a theorem, a proof is required, that is, a line of reasoning from axioms in the system (and other, already established theorems) to the given statement must be demonstrated. (38 words)

The notion of provability itself can also be encoded by Gödel numbers, in the following way: since a proof is a list of statements which obey certain rules, the Gödel number of a proof can be defined. (37 words)

Example sentences (13)

The incompleteness theorems are about formal provability within these systems, rather than about "provability" in an informal sense.

The relationship between provability in classical (or nonconstructive) systems and provability in intuitionistic (or constructive, respectively) systems is of particular interest.

They are particularly concerned with the interpretation of a Gödel sentence for an ω-inconsistent system as actually saying "I am not provable", since the system has no models in which the provability predicate corresponds to actual provability.

Also, it makes the concept of "provability," and thus of "theorem," a clear concept that only depends on the chosen system of axioms of the theory, and not on the choice of a proof system.

Crucially, because the system can support reasoning about properties of numbers, the results are equivalent to reasoning about provability of their equivalent statements.

Gödel was a platonist and therefore had no problems with asserting the truth and falsehood of statements independent of their provability.

In the course of his research, Gödel discovered that although a sentence which asserts its own falsehood leads to paradox, a sentence that asserts its own non-provability does not.

Provability and theoremhood To establish a mathematical statement as a theorem, a proof is required, that is, a line of reasoning from axioms in the system (and other, already established theorems) to the given statement must be demonstrated.

Advertentie

Questions about the provability of statements are represented as questions about the properties of numbers, which would be decidable by the theory if it were complete.

Questions about the provability of statements within the system are represented as questions about the arithmetical properties of numbers themselves, which would be decidable by the system if it were complete.

Rather than depend on provability of these axioms, science depends on the fact that they have not been objectively falsified.

The name Bew is short for beweisbar, the German word for "provable"; this name was originally used by Gödel to denote the provability formula just described.

The notion of provability itself can also be encoded by Gödel numbers, in the following way: since a proof is a list of statements which obey certain rules, the Gödel number of a proof can be defined.

Advertentie

Common combinations with provability

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "provability" in a sentence?
An example: "The incompleteness theorems are about formal provability within these systems, rather than about "provability" in an informal sense." This page contains 10+ example sentences with the word "provability" from authentic English texts.
What does "provability" mean?
Provability means: The condition of being provable
What are synonyms of "provability"?
Common synonyms of "provability" include: demonstrability, indisputability, indubitability, unquestionability, unquestionableness.
How many example sentences with "provability" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "provability", drawn from a database of millions of English sentences.