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On this page you'll find 10+ example sentences with Skolem. Discover how to use the word correctly in a sentence.

Rare word

Skolem in a sentence

Using Skolem

  • In the example corpus, skolem often appears in combinations such as: löwenheim skolem, skolem theorem.

Context around Skolem

  • Average sentence length in these examples: 23.4 words
  • Position in the sentence: 7 start, 6 middle, 0 end
  • Sentence types: 13 statements, 0 questions, 0 exclamations

Often before:

accepted 2×

Often after:

theorem 7× presented 1× noether 1×

Sentence patterns with Skolem

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

never accepted skolem s formulation 2× affirmative as skolem in 1933 1× review of skolem s paper 1× skolem presented a 1× stated that skolem s considerations 1× the löwenheim skolem theorem 1919 1× the löwenheim skolem theorem and 1× the löwenheim skolem theorem can 1×

Sentence openings and endings

Common sentence openings:

the löwenheim skolem 3× zermelo himself never 2× expressiveness the löwenheim 1× he established two 1× in the same 1× skolem presented a 1×

Common sentence endings:

first order logic 3× a nonstandard model 1× algebra is inner 1× all infinite cardinalities 1× each infinite cardinality 1× model is countable 1×

Words around Skolem

Just before it in the word index:

skole 2 skol 8 skokie 31 skogstad 2 skoglund 5 skogland 5

Just after it in the word index:

skolfield 4 skolkovo 2 skoll 18 skolnick 4 skolnik 4 skolt 3

Similar in corpus frequency:

aami 16 abada 16 abbottabad 16 abdulkareem 16 abha 16 abominations 16

Corpus analysis for Skolem

  • In this selection, "skolem" usually appears near the start of the sentence. The average example has 23.4 words, and this corpus slice is mostly made up of statements.
  • Around the word, accepted, theorem, presented and noether stand out and add context to how "skolem" is used.
  • Recognizable usage signals include never accepted skolem s formulation and affirmative as skolem in 1933. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "skolem" sits close to words such as aami, abada and abbottabad, which helps place it inside the broader word index.

Example types with skolem

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

Zermelo himself never accepted Skolem's formulation of the axiom schema of replacement. (13 words)

The Skolem–Noether theorem states any automorphism of a central simple algebra is inner. (14 words)

The Löwenheim-Skolem theorem can be used to show that this minimal model is countable. (15 words)

Longer example sentences

Skolem presented a resolution in terms of first-order definable replacements: "Let U be a definite proposition that holds for certain pairs (a, b) in the domain B; assume further, that for every a there exists at most one b such that U is true. (45 words)

He established two theorems for systems of this type: * A logical system satisfying Lindström's definition that contains first-order logic and satisfies both the Löwenheim–Skolem theorem and the compactness theorem must be equivalent to first-order logic. (39 words)

The Löwenheim–Skolem theorem (1919) showed that if a set of sentences in a countable first-order language has an infinite model then it has at least one model of each infinite cardinality. (33 words)

Example sentences (13)

In the same year, Fraenkel wrote a review of Skolem's paper, in which Fraenkel simply stated that Skolem’s considerations correspond to his own.

Expressiveness The Löwenheim–Skolem theorem shows that if a first-order theory has any infinite model, then it has infinite models of every cardinality.

He established two theorems for systems of this type: * A logical system satisfying Lindström's definition that contains first-order logic and satisfies both the Löwenheim–Skolem theorem and the compactness theorem must be equivalent to first-order logic.

Skolem presented a resolution in terms of first-order definable replacements: "Let U be a definite proposition that holds for certain pairs (a, b) in the domain B; assume further, that for every a there exists at most one b such that U is true.

The answer is affirmative as Skolem in 1933 provided an explicit construction of such a nonstandard model.

The Löwenheim–Skolem theorem (1919) showed that if a set of sentences in a countable first-order language has an infinite model then it has at least one model of each infinite cardinality.

The Löwenheim-Skolem theorem can be used to show that this minimal model is countable.

The Löwenheim–Skolem theorem implies that infinite structures cannot be categorically axiomatized in first-order logic.

Advertentie

The Skolem–Noether theorem states any automorphism of a central simple algebra is inner.

The upward Löwenheim–Skolem theorem shows that there are nonstandard models of PA of all infinite cardinalities.

When first-order logic without equality is studied, it is necessary to amend the statements of results such as the Löwenheim–Skolem theorem so that only normal models are considered.

Zermelo himself never accepted Skolem's formulation of the axiom schema of replacement.

Zermelo himself never accepted Skolem's formulation of ZFC using the language of first-order logic.

Advertentie

Common combinations with skolem

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "skolem" in a sentence?
An example: "In the same year, Fraenkel wrote a review of Skolem's paper, in which Fraenkel simply stated that Skolem’s considerations correspond to his own." This page contains 10+ example sentences with the word "skolem" from authentic English texts.
How many example sentences with "skolem" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "skolem", drawn from a database of millions of English sentences.