mathematics

Martin Goldstern

Martin Goldstern 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 Martin Goldstern rather than just read about it. In short: Martin Goldstern (born 7 May 1963 in Austria) is an Austrian mathematician and university professor for set theory at the TU Wien and head of the research unit 8 of the Institute of Discrete Mathematics and Geometry. His main research lies in set theory of the real line and forcing theory, and applications of set theory in universal algebra.

Key takeaways

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

Reference excerpt

Martin Goldstern (born 7 May 1963 in Austria) is an Austrian mathematician and university professor for set theory at the TU Wien and head of the research unit 8 of the Institute of Discrete Mathematics and Geometry. His main research lies in set theory of the real line and forcing theory, and applications of set theory in universal algebra. He is cousin of Martin Karplus and great-nephew of Eugenie Goldstern.

Academic career Goldstern earned a Ph.D. in 1986 at the TU Wien under the direction of Robert F. Tichy, with a dissertation in equidistribution; and another in set theory in 1991 at UC Berkeley under the direction of Jack Silver and Haim Judah. As postdoc he held temporary positions at Bar Ilan University, Freie Universität Berlin and Carnegie Mellon University. He acquired habilitation at TU Wien in 1993 with the thesis Tools for your forcing construction, which greatly simplified, and made widely accessible, a general preservation theorem of Saharon Shelah for countable support proper forcing iterations. In 1993 he started working at TU Wien, where he is now full professor. In 1996, Goldstern won the Prize of the Austrian Mathematical Society. In 2015, 2018 and 2023 he held visiting professor positions at the Hebrew University of Jerusalem. Together with Jakob Kellner and Shelah he showed the consistency (assuming large cardinals) of Cichoń's maximum, i.e., the statement that the ten "independent" entries in Cichoń's diagram are all different.

Selected publications Goldstern, Martin (1993). "Tools for your forcing construction" (PDF). Set theory of the reals (Ramat Gan, 1991). Israel Math. Conf. Proc. Vol. 6. Bar-Ilan Univ., Ramat Gan. pp. 305–360. Goldstern, Martin; Pinsker, Michael (1993), "A survey of clones on infinite sets", Algebra Universalis, 59 (3–4): 365–403, arXiv:math/0407173, doi:10.1007/s00012-008-2100-2, S2CID 16450005 Goldstern, Martin; Judah, Haim (1995). The incompleteness phenomenon. A new course in mathematical logic, With a foreword by Saharon Shelah. A K Peters, Ltd., Natick, MA. pp. xiv+247. ISBN 9781568810294. (reprinted in 1998) Goldstern, Martin; Kellner, Jakob; Shelah, Saharon (2019), "Cichoń's maximum", Annals of Mathematics, 190 (1): 113–143, arXiv:1708.03691, doi:10.4007/annals.2019.190.1.2, S2CID 119654292 Goldstern, Martin; Kellner, Jakob; Mejía, Diego A.; Shelah, Saharon (2019), "Cichoń's maximum without large cardinals", Journal of the European Mathematical Society, 24 (11): 3951–3967, arXiv:1906.06608, doi:10.4171/JEMS/1178, S2CID 189928245

References

External links Goldstern's web page at TU Wien Martin Goldstern at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Martin Goldstern

Start with the simplest possible case. Write down what Martin Goldstern 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 Martin Goldstern 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 Martin Goldstern 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 Martin Goldstern

In research: Martin Goldstern 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 Martin Goldstern 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: Martin Goldstern is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1963 births, 20th-century Austrian mathematicians, 21st-century Austrian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Martin Goldstern 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 Martin Goldstern in 20 minutes

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

Frequently asked questions

What is Martin Goldstern in simple terms?

Why does Martin Goldstern 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 Martin Goldstern?

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 Martin Goldstern.