# Tagged Questions

**6**

votes

**1**answer

307 views

### Different approaches to forcing

There are many different approaches to the forcing method, and I am looking for all known such approaches. So my question is:
Question 1. Which different approaches to set theoretic forcing are ...

**6**

votes

**0**answers

215 views

### Silver's unpublished work on reverse Easton iteration

Silver was the first person who used the method of reverse Easton iterations in connection with large cardinals, and used it to force the failure of $GCH$ at some measurable cardinal.
At most papers ...

**20**

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**2**answers

742 views

### construction of nonmeasurable sets

I have a history question for which I've had trouble finding a good answer.
The common story about nonmeasurable sets is that Vitali showed that one existed using the Axiom of Choice, and Lebesgue et ...

**10**

votes

**1**answer

301 views

### Elements of the method of forcing in some papers of N. N. Luzin

In the paper
Eléments de la méthode de forcing dans quelques travaux de N. N. Lousin. (French) [Elements of the method of forcing in some papers of N. N. Luzin] Amphora, 469–479, Birkhäuser, ...

**9**

votes

**2**answers

424 views

### Origin of the term “generic” in set theory

In set theory, in particular the context of forcing, if $M$ is a model of $\sf ZFC$ and $P\in M$ is a partial order, we say that $G\subseteq P$ is a generic filter (or $M$-generic or generic over $M$) ...

**2**

votes

**3**answers

549 views

### The Hidden Aspect of Set Theory [closed]

This question is inspired by a similar question at the beginning of Kunen's new book, "Set Theory".
Many mathematicians believe they are exploring a "real" universe. In such a Platonic point of ...

**7**

votes

**2**answers

521 views

### $\aleph$ looks like $\mathbb N$?

We all know the notation $\aleph_\lambda$ for the $\lambda$th (or, I guess, $\lambda+1$st) infinite cardinal number; in particular $\aleph_0$ is the cardinality of the the set of natural numbers ...

**4**

votes

**1**answer

482 views

### Origin of “Woodin cardinal”

Sorry if this is a completely stupid question (I'm a not a set-theorist, though I've been doing some reading in the subject), but I was wondering, specifically, about the exact provenance of the name. ...

**18**

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**2**answers

2k 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 ...

**12**

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**6**answers

1k views

### The origins of forcing in mathematical logic and other branches of mathematics

As everyone knows, forcing was created by Cohen to answer questions in set theory.
Question 1. What are the first applications of set theoretic forcing in other branches of mathematical logic, like ...

**12**

votes

**3**answers

899 views

### When was the continuum hypothesis born?

The question Solutions to the Continuum Hypothesis states that the continuum hypothesis was posed by Cantor in 1890. In http://en.wikipedia.org/wiki/Continuum_hypothesis the year 1878 is quoted ...

**21**

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**2**answers

1k views

### Hahn's Embedding Theorem and the oldest open question in set theory

Hans Hahn is often credited with creating the modern theory of ordered algebraic systems with the publication of his paper Über die nichtarchimedischen Grössensysteme (Sitzungsberichte der ...

**21**

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**2**answers

1k views

### Similarities between Post's Problem and Cohen's Forcing

Remark: I have since learned that G.H. Moore addresses this question in the third reference listed at the end of this post, beginning on p. 157 in which he cites a letter from Kreisel to Gödel dated ...

**35**

votes

**4**answers

2k views

### The origin of sets?

The history of set theory from Cantor to modern times is well documented. However, the origin of the idea of sets is not so clear. A few years ago, I taught a set theory course and I did some digging ...

**3**

votes

**0**answers

245 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 ...

**8**

votes

**1**answer

756 views

### 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 ...

**8**

votes

**1**answer

463 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 ...

**48**

votes

**12**answers

9k views

### Logic in mathematics and philosophy

What are the relations between logic as an area of (modern) philosophy and mathematical logic.
The world "modern" refers to 20th century and later, and I am curious mainly about the second half of ...

**4**

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**4**answers

1k views

**11**

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**4**answers

851 views

### Russell and Whitehead's types: ramified and unramified

I was reading Logicomix (a fictionalised account of logic from Frege to Gödel through Russell's eyes) and there was mention about two different versions of types developed by Russell and Whitehead for ...

**11**

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**4**answers

1k views

### Earliest diagonal proof of the uncountability of the reals.

I cited the diagonal proof of the uncountability of the reals as an example of a `common false belief' in mathematics, not because there is anything wrong with the proof but because it is commonly ...

**3**

votes

**1**answer

423 views

### What are the oldest illustrations of “Venn” diagrams?

Graphical representations of intersection of sets as logical combinations are much older than Venn.
Euler and Leibniz are often quoted and the current Wikipedia article also quotes Ramon Llull but I ...

**32**

votes

**5**answers

3k 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 ...