mathematics

Moti Gitik

Moti Gitik 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 Moti Gitik rather than just read about it. In short: Moti Gitik (Hebrew: מוטי גיטיק) is a mathematician, working in set theory, who is professor at the Tel-Aviv University. He was an invited speaker at the 2002 International Congresses of Mathematicians, and became a fellow of the American Mathematical Society in 2012.

Key takeaways

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

Reference excerpt

Moti Gitik (Hebrew: מוטי גיטיק) is a mathematician, working in set theory, who is professor at the Tel-Aviv University. He was an invited speaker at the 2002 International Congresses of Mathematicians, and became a fellow of the American Mathematical Society in 2012.

Research Gitik proved the consistency of "all uncountable cardinals are singular" (a strong negation of the axiom of choice) from the consistency of "there is a proper class of strongly compact cardinals". He further proved the equiconsistency of the following statements:

There is a cardinal κ with Mitchell order κ++. There is a measurable cardinal κ with 2κ > κ+. There is a strong limit singular cardinal λ with 2λ > λ+. The GCH holds below ℵω, and 2ℵω=ℵω+2. Gitik discovered several methods for building models of ZFC with complicated Cardinal Arithmetic structure. His main results deal with consistency and equi-consistency of non-trivial patterns of the Power Function over singular cardinals.

Selected publications Gitik, Moti (1986). "Changing Cofinalities and the Nonstationary Ideal". Israel Journal of Mathematics. 56 (3): 280–314. doi:10.1007/BF02782938. Gitik, Moti (1991). "The strength of the failure of the singular cardinal hypothesis". Annals of Pure and Applied Logic. 51 (3): 215–240. doi:10.1016/0168-0072(91)90016-F. Gitik, Moti; Magidor, Menachem (1992). "The Singular Cardinal Hypothesis Revisited". Set Theory of the Continuum. Mathematical Sciences Research Institute Publications. Vol. 26. pp. 243–279. doi:10.1007/978-1-4613-9754-0_16. ISBN 978-1-4613-9756-4. Gitik, Moti (1996). "Blowing up the power of a singular cardinal". Annals of Pure and Applied Logic. 80 (1): 17–33. arXiv:math/9404204. doi:10.1016/0168-0072(95)00046-1. Gitik, Moti (2020). "Extender based forcings with overlapping extenders and negations of the Shelah Weak Hypothesis". Journal of Mathematical Logic. 20 (3): 2050013. doi:10.1142/S0219061320500130. S2CID 46948714.

References

External links Moti Gitik at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Moti Gitik

Start with the simplest possible case. Write down what Moti Gitik 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 Moti Gitik 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 Moti Gitik 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 Moti Gitik

In research: Moti Gitik 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 Moti Gitik 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: Moti Gitik is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century Israeli mathematicians, 21st-century Israeli mathematicians, Academic staff of Tel Aviv University, so understanding it makes those chapters shorter.
In everyday life: Look for Moti Gitik 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 Moti Gitik in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Moti Gitik 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 Moti Gitik out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Moti Gitik in simple terms?

Why does Moti Gitik 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 Moti Gitik?

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 Moti Gitik.