Questions tagged [bourbaki]

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55
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4answers
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Bourbaki's definition of the number 1

According to a polemical article by Adrian Mathias, Robert Solovay showed that Bourbaki's definition of the number 1, written out using the formalism in the 1970 edition of Théorie des Ensembles, ...
4
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0answers
150 views

Bar notation in Bourbaki’s *Lie groups*, Chap. IX

I am looking at Chapter IX (Compact Real Lie Groups), §4, Exercise 8 (translation). Given a complex subspace $\mathfrak p$ in the complexification $\mathfrak g_{\mathbf C}$ of some $\mathfrak g$, they ...
3
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1answer
579 views

Why Bourbaki's epsilon-calculus is not suitable for set theory?

Does anybody shed light on what is A. R. D. Mathias' idea that Bourbaki's $\tau$-calculus (Logically the same as Hilbert's $\varepsilon$-calculus) is not suitable for set theory, especially because of ...
8
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1answer
1k views

Who invented Monoid?

I was trying to find (and failed) the original author of either the concept of Monoid (set with binary associative operation and identity) the name (which sounds french ? and also Dioid (for what ...
4
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4answers
1k views

Reference request: any 20th century German critiques of Bourbaki? [closed]

Vladimir Arnold is known, among other things, for offering a scathing critique of Bourbaki: The Arnold – Serre debate Recently I've been reading some Nietzsche, and he chides some Germans in the ...
2
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0answers
126 views

Noether’s “set theoretic foundations” of algebra. Reference

In [C Mclarty] we read [Noether] project was to get abstract algebra away from thinking about operations on elements, such as addition or multiplication of elements in groups or rings. Her algebra ...
9
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3answers
1k views

Where is Seminaire Bourbaki on-line?

Where is Seminaire Bourbaki on-line? The reason I ask is that for years it was complicated-enough already to find it in traditional libraries, as it would be catalogued according to its venue or ...
3
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2answers
535 views

formalisation of Bourbaki, General Topology

Is there a formalisation of Bourbaki, General Topology book, particularly its first chapter? Are there formal proofs of elementary topology arguments such as a Hausdorff compact space is ...
2
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1answer
821 views

Reference for Connes Bourbaki membership or otherwise

Alain Connes being a leading French mathematician today one could ask whether he is a member of the Bourbaki group. Is there a published reference that would either refute or confirm this?
29
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0answers
2k views

Greatly expanded new edition of a Bourbaki chapter on algebra?

Recently I discovered by accident that Bourbaki issued in 2012 a radically expanded version of their 1958 Chapter 8 Modules et anneaux semi-simples (like other chapters, initially in French) within ...
61
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4answers
9k views

The Arnold – Serre debate

I have read (but I cannot now find where) that V. I. Arnold & J.-P. Serre had a public debate on the value of Bourbaki. Does anyone have more details, or remember or know what was said?
17
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0answers
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Why did Bourbaki not use universal algebra?

I have seen a discussion about Bourbaki’s usage of categories before. So let me ask a different question: why did he not use universal algebra? Well, universal algebra is not much older than category ...
27
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5answers
7k views

Why did Bourbaki's Élements omit the theory of categories?

QUESTION They had plenty of time to adopt the theory of categories. They had Eilenberg, then Cartan, then Grothendieck. Did they feel that they have established their approach already, that it's too ...
4
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1answer
1k views

Elements of the history of mathematics

Is it known who actually wrote Bourbaki's Elements of the History of Mathematics?
2
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0answers
743 views

Regarding a proof in Bourbaki's Topological Vector Spaces

On Bourbaki's TVS Chapter IV pages 33-34, the last part of Proposition 2 can be formulated as follows: Notations: $K$ - The underlying field which is the real or complex number field; $X$ - A ...
0
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2answers
1k views

Possible errata in Nicolas Bourbaki's General Topology -I, Chapter 1 Exercise 2 ?

Here is the text of Exercise: 2 a) Let $X$ be an ordered set. Show that the set of intervals $\left[x, \rightarrow\right[$ (resp. $\left]\leftarrow, x\right]$) is a base of topology on $X$; ...
4
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1answer
836 views

Is there any relationship between Bourbaki's Epsilon Calculus and Lambda Calculus? Is $\lambda x$ the same as $\tau_x$?

Is there any relationship between Bourbaki's Epsilon Calculus and Lambda Calculus ? Whether $\lambda {x}$ is same as $\tau _{x}$ ? Are the rules of Meta-Mathematics (Criteria of Substitution, ...
5
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1answer
945 views

Bourbaki theory of isomorphism, examples of untransportable formulas

In their book "Theory of sets" Bourbaki suggested a general theory of isomorphism. (See also http://www.tau.ac.il/~corry/publications/articles/pdf/bourbaki-structures.pdf ) The example of an ...
6
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7answers
1k views

The isomorphism inference rule

Suppose we are writing very detailed proofs, absolutely without any gaps (for example, for checking proofs by computer). In such formal proofs every step (even a trivial one) must be justified. For ...
16
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4answers
4k views

Bourbaki's epsilon-calculus notation

Bourbaki used a very very strange notation for the epsilon-calculus consisting of $\tau$s and $\blacksquare$. In fact, that box should not be filled in, but for some reason, I can't produce a \Box. ...
37
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5answers
5k views

Were Bourbaki committed to set-theoretical reductionism?

A set-theoretical reductionist holds that sets are the only abstract objects, and that (e.g.) numbers are identical to sets. (Which sets? A reductionist is a relativist if she is (e.g.) indifferent ...