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Explore Fraenkel through 10+ example sentences from English. Ideal for language learners, writers and word enthusiasts.

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Fraenkel in a sentence

Using Fraenkel

  • In the example corpus, fraenkel often appears in combinations such as: zermelo fraenkel, fraenkel axioms, fraenkel horace.

Context around Fraenkel

  • Average sentence length in these examples: 24.4 words
  • Position in the sentence: 12 start, 4 middle, 4 end
  • Sentence types: 20 statements, 0 questions, 0 exclamations

Often before:

zermelo 9× year 1× adolf 1× eduard 1×

Often after:

horace 6× axioms 5× set 4× wrote 1× simply 1× remarked 1× axiomatized 1×

Sentence patterns with Fraenkel

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

of zermelo fraenkel set theory 3× the zermelo fraenkel axioms 2× by adolf fraenkel in 1922 1× e fraenkel horace 14 1× e fraenkel horace 15 1× e fraenkel horace 2 1× e fraenkel horace 23 1× e fraenkel horace 32 1×

Sentence openings and endings

Common sentence openings:

e fraenkel horace 6× arguments for and 1× ebbinghaus p 189 1× eduard fraenkel remarked 1× for this reason 1× fraenkel s 1922 1×

Common sentence endings:

zermelo fraenkel axioms 2× and explicit politics 1× can be useful 1× for helpful arguments 1× for set theory 1× hypothesis must hold 1×

Words around Fraenkel

Just before it in the word index:

frady 7 fradon 3 fradkin 2 fradgley 6 fractus 6 fracturing 125

Just after it in the word index:

frag 7 fraga 11 fragasso 3 fragebogen 2 fragging 4 fraggle 2

Similar in corpus frequency:

abbe 37 abeyance 37 abp 37 achiever 37 acker 37 acquiescence 37

Corpus analysis for Fraenkel

  • In this selection, "fraenkel" usually appears near the start of the sentence. The average example has 24.4 words, and this corpus slice is mostly made up of statements.
  • Around the word, zermelo, year, adolf, horace, axioms and set stand out and add context to how "fraenkel" is used.
  • Recognizable usage signals include of zermelo fraenkel set theory and the zermelo fraenkel axioms. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "fraenkel" sits close to words such as abbe, abeyance and abp, which helps place it inside the broader word index.

Example types with fraenkel

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

Fraenkel's 1922 publication thanked Zermelo for helpful arguments. (9 words)

E. Fraenkel, Horace, p. 309 Such refinement of style was not unusual for Horace. (14 words)

Its publication by Adolf Fraenkel in 1922 is what makes modern set theory Zermelo-Fraenkel set theory (ZFC). (18 words)

Longer example sentences

Because there are models of Zermelo–Fraenkel set theory of interest to set theorists that satisfy the axiom of dependent choice but not the full axiom of choice, the knowledge that a particular proof only requires dependent choice can be useful. (41 words)

Gödel showed that the continuum hypothesis cannot be disproven from the axioms of Zermelo–Fraenkel set theory (with or without the axiom of choice), by developing the constructible universe of set theory in which the continuum hypothesis must hold. (39 words)

Arguments for and against CH Gödel believed that CH is false and that his proof that CH is consistent with ZFC only shows that the Zermelo–Fraenkel axioms do not adequately characterize the universe of sets. (36 words)

Example sentences (20)

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.

Its publication by Adolf Fraenkel in 1922 is what makes modern set theory Zermelo-Fraenkel set theory (ZFC).

Arguments for and against CH Gödel believed that CH is false and that his proof that CH is consistent with ZFC only shows that the Zermelo–Fraenkel axioms do not adequately characterize the universe of sets.

Because there are models of Zermelo–Fraenkel set theory of interest to set theorists that satisfy the axiom of dependent choice but not the full axiom of choice, the knowledge that a particular proof only requires dependent choice can be useful.

Both of these results assume that the Zermelo–Fraenkel axioms are consistent; this assumption is widely believed to be true.

Ebbinghaus, p. 189 Zermelo and Fraenkel had corresponded heavily in 1921; the axiom of replacement was a major topic of this exchange.

Eduard Fraenkel remarked : p. 11, note 6 citation on the powerful contrasts between declaimed and sung dialogue in this scene.

E. Fraenkel, Horace, 14–15 It was about this time that he began writing his Satires and Epodes.

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E. Fraenkel, Horace, 15 It signalled his identification with the Octavian regime yet, in the second book of Satires that soon followed, he continued the apolitical stance of the first book.

E. Fraenkel, Horace, 2–3 Such state-sponsored migration must have added still more linguistic variety to the area.

E. Fraenkel, Horace, 23 Works Odes 1.14 - Wall poem in Leiden The dating of Horace's works isn't known precisely and scholars often debate the exact order in which they were first 'published'.

E. Fraenkel, Horace, 32, 80 Lucilius was a rugged patriot and a significant voice in Roman self-awareness, endearing himself to his countrymen by his blunt frankness and explicit politics.

E. Fraenkel, Horace, p. 309 Such refinement of style was not unusual for Horace.

For this reason, the axiom schema of separation is often left out of modern lists of the Zermelo–Fraenkel axioms.

Fraenkel's 1922 publication thanked Zermelo for helpful arguments.

Furthermore, using techniques of forcing ( Cohen ) one can show that the continuum hypothesis (Cantor) is independent of the Zermelo–Fraenkel axioms.

Fuzzy set theory main In set theory as Cantor defined and Zermelo and Fraenkel axiomatized, an object is either a member of a set or not.

Gödel showed that the continuum hypothesis cannot be disproven from the axioms of Zermelo–Fraenkel set theory (with or without the axiom of choice), by developing the constructible universe of set theory in which the continuum hypothesis must hold.

However, at present, there is no known way of demonstrating the consistency of the modern Zermelo–Fraenkel axioms for set theory.

In 1963, Paul Cohen showed that the continuum hypothesis cannot be proven from the axioms of Zermelo–Fraenkel set theory (Cohen 1966).

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Common combinations with fraenkel

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "fraenkel" 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 "fraenkel" from authentic English texts.
How many example sentences with "fraenkel" are there?
Voorbeeldzinnen.info contains at least 10+ example sentences with "fraenkel", drawn from a database of millions of English sentences.