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Questions tagged [set-theory]

For questions about the mathematical branch that is based on the study of sets, i.e. collections of objects.

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Did Kronecker say that set theory is not mathematics?

I have frequently come across Kronecker's statement about set theory: I don't know what predominates in Cantor's theory - philosophy or theology, but I am sure that there is no mathematics there. It ...
Franz Kurz's user avatar
5 votes
0 answers
226 views

What was Zermelo's _reception_ of von Neumann's definition of ordinal numbers?

Redactional note Like suggested by one of this question's (or so I understand the meta.discussion), this question should be given some too-many-subquestions-redacting, in particular since the easiest ...
Peter Heinig's user avatar
5 votes
0 answers
513 views

Why is ZFC used more widely than NBG?

In studying the solutions proposed for Russell's Paradox on naive set theory (mainly the corresponding entry in the Stanford Encyclopedia of Philosophy) I came across the following considerations: von ...
Luc M's user avatar
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Who proposed terminating decimals as a major set and why are them important in France?

After looking at some school sources in French, it is common to provide the various number sets in the following order $$\mathbb{N}\subset \mathbb{Z}\subset\mathbb{D}\subset\mathbb{Q}\subset\mathbb{R}\...
Mauricio's user avatar
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4 votes
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What role has Whitehead's Conjecture played in the thinking on the plurality of set theories?

I am curious about the history of the Whitehead's Conjecture, as this was the first natural mathematical statement, in the sense that mathematicians were actually interested in the answer, that was ...
Mozibur Ullah's user avatar
4 votes
0 answers
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Kreisel on "set" as a coherent idea

In his paper Two notes on the foundations of set-theory, Kreisel begins: Recall that, naively, sets present themselves in a number of distinct contexts. [...] One may therefore doubt whether any ...
Noah Schweber's user avatar
3 votes
0 answers
229 views

where does trace $\sigma$-algebra come from

I came across the term trace $\sigma$-algebra in the context of conditional probability. Does anyone know where it comes from? i found a reference to trace of a matrix here: https://mathshistory.st-...
TonyK's user avatar
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3 votes
0 answers
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Translations of "Sur le théorème de Zorn"?

Are there any translations of the following into English, German, or Russian? Nicolas Bourbaki, Sur le théorème de Zorn, Archiv der Mathematik, Volume 2, pages 434–437, November 1949. Any help is ...
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2 votes
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What were Cantor’s “real numbers of higher type”?

In the preamble to “Essays on the Theory of Numbers”, Dedekind makes passing reference to a theory (expounded in Cantor’s “Ueber die Ausdenung eines Satzes aus der Theorie der trigonometrischen Reihen”...
James Propp's user avatar
2 votes
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Was there a view of a figure as a set of points before set theory?

A circle can be written as the solution set of an equation $x^2+y^2=1$. I have heard that Fermat associated figures with equations in the 17th century. Did people see figures as sets of points before ...
BonBon's user avatar
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Zermelo's or Fraenkel's early consideration of something equivalent to countable Replacement

I have now claimed a few times on the internet, based on something (sensible!) I read, that at some point in the 1920s, that Zermelo at one point considered as a set theoretic axiom (schema) something ...
David Roberts's user avatar
2 votes
0 answers
97 views

The definition of 'countable' and 'finite' set

I have an equivalent definition of finite and countable sets that seems 'less' based on set theory than the usual definitions. I am wondering if anyone has encountered these definitions anywhere, esp....
Sam Sanders's user avatar
2 votes
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107 views

Where can I find the actual first order formulation of ZFC Axioms?

I'm currently writing my thesis about ZFC origins, and I need a source from where to know who gives the actual first order formulation of ZFC. I got to the point where Bernays writes about it and ...
TransfiniteGuy's user avatar
2 votes
0 answers
254 views

Set Theory, onto and into their relation to spoken language definitions

Does anyone know how the definitions for onto and into map to the spoken language definitions of the words? I compared the Bourbaki definitions to these words and have a suspicion that the German ...
Nick's user avatar
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Whence Whitehead's essence?

In the article Quine’s New Foundations of The Stanford Encyclopedia of Philosophy (Summer 2019 Edition), Thomas Forster writes: In [1944] Hailperin gave the first of a number of finite ...
Frode Alfson Bjørdal's user avatar
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Who was the first to use bijections?

I know that Bourbaki were the first who used the word 'bijection', but one-to one functions were for sure used before them. So do you aware of the earliest examples of one-to-one correspondences?
kerzol's user avatar
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What are Gödel's property theories

The opening sentence of Roger Myhill's article Paradoxes, in Synthese 60 (1984), 129-143, is: “Gödel said to me more than once "There never were any set-theoretic paradoxes, but the property-...
Frode Alfson Bjørdal's user avatar
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372 views

Has Cantor's irregular enumeration of rationals ever been discussed?

Enumeration of all positive fractions recently has gained renewed interest (see the list below). By translation invariance we can be sure that in all intervals (n, n+1] of the real axis, there are the ...
Franz Kurz's user avatar
-2 votes
1 answer
225 views

Endorsers of the method of well-ordering reported by Hausdorff?

In the course of preparing a lecture for graduate students about errors of early set theory I have come across this nice example reported by Hausdorff which violates Peano's successor axiom but ...
Franz Kurz's user avatar