mathematics

Vladimir Kanovei

Vladimir Kanovei is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Vladimir Kanovei rather than just read about it. In short: Vladimir G. Kanovei (born 1951) is a Russian mathematician working at the Institute for Information Transmission Problems in Moscow, Russia.

Key takeaways

Vladimir Kanovei belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Vladimir Kanovei to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Vladimir Kanovei from memory before moving on to harder problems.

Reference excerpt

Vladimir G. Kanovei (born 1951) is a Russian mathematician working at the Institute for Information Transmission Problems in Moscow, Russia. His interests include mathematical logic and foundations, as well as mathematical history.

Selected publications Kanovei, Vladimir; Katz, Mikhail G.; Mormann, Thomas (2013), "Tools, Objects, and Chimeras: Connes on the Role of Hyperreals in Mathematics", Foundations of Science, 18 (2): 259–296, arXiv:1211.0244, doi:10.1007/s10699-012-9316-5, S2CID 254515019. Kanovei, Vladimir; Reeken, Michael; Nonstandard analysis, axiomatically. Springer Monographs in Mathematics. Springer-Verlag, Berlin, 2004. xvi+408 pp. ISBN 3-540-22243-X Kanovei, Vladimir; Borel equivalence relations. Structure and classification. University Lecture Series, 44. American Mathematical Society, Providence, RI, 2008. x+240 pp. ISBN 978-0-8218-4453-3 Kanoveĭ, V.; Reeken, M.; On Ulam's problem concerning the stability of approximate homomorphisms. (Russian) Tr. Mat. Inst. Steklova 231 (2000), Din. Sist., Avtom. i Beskon. Gruppy, 249–283; translation in Proc. Steklov Inst. Math. 2000, no. 4 (231), 238–270 Kanoveĭ, V. G.; Lyubetskiĭ, V. A.; On some classical problems in descriptive set theory. (Russian) Uspekhi Mat. Nauk 58 (2003), no. 5(353), 3--88; translation in Russian Math. Surveys 58 (2003), no. 5, 839–927 Kanoveĭ, V. G.; Reeken, M.; Some new results on the Borel irreducibility of equivalence relations. (Russian) Izv. Ross. Akad. Nauk Ser. Mat. 67 (2003), no. 1, 59–82; translation in Izv. Math. 67 (2003), no. 1, 55–76 03E15 (54H05) Kanovei, Vladimir; Reeken, Michael; Mathematics in a nonstandard world. II. Math. Japon. 45 (1997), no. 3, 555–571. Kanovei, Vladimir; On non-wellfounded iterations of the perfect set forcing. Journal of Symbolic Logic 64 (1999), no. 2, 551–574. Kanovei, Vladimir; Shelah, Saharon; A definable nonstandard model of the reals. Journal of Symbolic Logic 69 (2004), no. 1, 159–164. Kanovei, Vladimir; Reeken, Michael. Internal approach to external sets and universes. I. Bounded set theory. Studia Logica 55 (1995), no. 2, 229–257. Kanovei, Vladimir; Reeken, Michael. Internal approach to external sets and universes. II. External universes over the universe of bounded set theory. Studia Logica 55 (1995), no. 3, 347–376. Kanovei, Vladimir; Reeken, Michael. Internal approach to external sets and universes. III. Partially saturated universes. Studia Logica 56 (1996), no. 3, 293–322. This series of three papers was reviewed by Karel Hrbacek here.

External links Home page

Worked examples

Example 1 — a first encounter with Vladimir Kanovei

Start with the simplest possible case. Write down what Vladimir Kanovei claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Vladimir Kanovei before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Vladimir Kanovei ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Vladimir Kanovei

In research: Vladimir Kanovei appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Vladimir Kanovei in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Vladimir Kanovei is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1951 births, Living people, Model theorists, so understanding it makes those chapters shorter.
In everyday life: Look for Vladimir Kanovei outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Vladimir Kanovei in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Vladimir Kanovei means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Vladimir Kanovei out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Vladimir Kanovei in simple terms?

Vladimir G. Kanovei (born 1951) is a Russian mathematician working at the Institute for Information Transmission Problems in Moscow, Russia.

Why does Vladimir Kanovei matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Vladimir Kanovei?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Vladimir Kanovei.