All Questions
6 questions
15
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1
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Where did Zermelo first model the natural numbers by iterates of the singleton operator, and have the definitions been compared by himself?
E. Zermelo is widely said to have modelled the (axioms of the) natural numbers by iterating the singleton operation $\{\cdot\}\colon \mathsf{Set}\rightarrow\mathsf{Set}$, $S\mapsto\{S\}$, whence the ...
- 6,051
17
votes
2
answers
2k
views
Why did Gödel name his constructible universe $L$?
It seems like Gödel didn't use the letter $L$ for his model before his book "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory", which is ...
- 1,170
22
votes
2
answers
3k
views
Where are Georg Cantor's Original Manuscripts?
Georg Cantor is famous for introducing transfinite numbers and set theory.
A main part of his mathematical point of view about this new type of "numbers" and this new "realm of mathematics" cannot be ...
- 229
3
votes
0
answers
342
views
A Question Regarding Boolean-valued Models
What were the intuitions motivating the creation (or discovery, if you will) of Boolean-valued models? I have searched for the Scott-Solovay paper on the subject, but to no avail. There also seems to ...
- 6,132
13
votes
1
answer
2k
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Hausdorff and Naive Set Theory
Erhard Scholz, in his article "Felix Hausdorff and the Hausdorff edition" writes the following:
"Hausdorff considered the contemporary attempts to secure axiomatic foundations for set theory as ...
- 6,132
9
votes
1
answer
918
views
What is the etymology of zero-sharp?
I have wondered for a while what gave rise to the notation $0^\sharp$. According to wikipedia this is due to Solovay in 1967, but (perhaps unsurprisingly) there's no discussion of why that notation ...
- 437