# Tagged Questions

**15**

votes

**1**answer

820 views

### Gödel's Constructible Universe in Infinitary Logics (A Possible Approach to HOD Problem)

Gödel's constructible universe ($L$) is defined using definable power set operator in first order logic ($\mathcal{L}_{\omega ,\omega}$). One can produce such a universe in infinitary logics in ...

**10**

votes

**1**answer

315 views

### V=HOD & The Height of the Large Cardinal Tree

As we know the assumption $V=L$ adds a restriction on the height of the large cardinal tree. Also there is a strict border like $0^{\sharp}$ exists such that all large cardinal axioms which are ...

**2**

votes

**1**answer

191 views

### What is the order type of $L$ with Godel's well ordering?

In some sense $Ord$ is a "proper class" ordinal. Unfortunately the notion of a proper class ordinal is not a straight forward generalization of the notion of "set" ordinals because the proper classes ...

**11**

votes

**0**answers

615 views

### Can a model of $V\neq L$ contain a class giving the $L$-ordering on all its sets?

This question is inspired by the excellent question by Douglas Ulrich When is $L$-Rank definable in inner models of $V=L$?
Suppose $M \in L$ is a countable model of $ZFC$, and furthermore suppose $M ...

**11**

votes

**2**answers

405 views

### Constructible models of New Foundations?

Hi all! Is there anything like GĂ¶del's constructible universe for New Foundations?
More precisely, I would like a process for taking a model $M$ of NF, and using it to build a model $L \subseteq M$ ...

**6**

votes

**1**answer

233 views

### Acceptability and Soundness of J-structures.

I would like an example of a J-structure $(J^A,B)$ which is not acceptable and one that is not 1-sound.
Edit:Let us recall that a structure $J^A_\alpha$ is acceptable if for every limit ordinal $ ...

**4**

votes

**1**answer

229 views

### Sequences of projecta in the constructible hierarchy.

For $n$ a natural number, $\alpha$ an ordinal, let $p(n,\alpha)$ be the $n$-th projectum of $J_\alpha$, where $J$ is the Jensen hierarchy for $L$.
Call a finite sequence $s:=(x_1,\dots,x_m)$ of ...