# Tagged Questions

**1**

vote

**0**answers

210 views

### If there is a Reinhardt cardinal, then there is one universe? [closed]

If there is a nontrivial elementary embedding $j:V \to V$, then there is a universe which contains all the large cardinals.
Is there such a universe? Does this imply there is one universe from ...

**2**

votes

**2**answers

985 views

### In What Sense is Set Theory a 'Foundation' for Mathematics? [closed]

In what sense is set theory a foundation for mathematics? To my mind (for what that is worth), there are at least three (somewhat) distinct senses in which set 'theory' (I put "theory" in scare ...

**0**

votes

**1**answer

106 views

### $\epsilon$-Formalization of Undecidability of CH

Can the statement
CH is not provable in ZFC
be formalized as en $\epsilon$-Formula $\phi$ s.t. $ZFC \vdash \phi $
If so why is it refered to as an "metatheorem".

**4**

votes

**1**answer

407 views

### Does ZF prove that a finite subtheory axiomatizes it over transitive proper class models?

If $\text{ZF}$ is consistent, then it is not finitely axiomatizable. For if $\Gamma$ is a finite axiomatization, then $\text{ZF}$ proves by reflection that $\Gamma$ has a set model, and hence (since ...

**10**

votes

**3**answers

1k views

### Are there natural examples of mathematical statements which follow from consistency statements?

Motivation
One of the methods for strictly extending a theory $T$ (which is axiomatizable and consistent, and includes enough arithmetic) is adding the sentence expressing the consistency of $T$ ( ...

**4**

votes

**1**answer

750 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 ...

**22**

votes

**8**answers

2k views

### Intuitive and/or philosophical explanation for set theory paradoxes

Every student of set theory knows that the early axiomatization of the theory
had to deal with spectacular paradoxes such as Russel's, Burali-Forti's etc.
This is why the (self-contradictory) ...

**6**

votes

**7**answers

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 ...