# Tag Info

Accepted

### Czelakowski's claimed proof of the Twin Prime Conjecture

The error in the paper is in the proof of Theorem 7.2. The proof of Theorem 7.2 is immediately suspicious because of how vague it is in places and because of how lofty the expository text before and ...
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### Czelakowski's claimed proof of the Twin Prime Conjecture

The Editor-in-Chief has released a statement on behalf of the journal retracting the papers, as follows. Public announcement Recently two articles on the applications of Rasiowa-Sikorski Lemma to ...

### Czelakowski's claimed proof of the Twin Prime Conjecture

From my reading, the only facts about the concept of twin primes used in the argument are that there exist pairs of numbers $n$ and $n+2$ (in the discussion after equation (8.4)) and there exist ...
• 138k
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### How to add essentially new knots to the universe?

Yes, forcing can add fundamentally new knots, not equivalent to any ground model knot. Indeed, whenever you extend the set-theoretic universe to add new reals, then you must also have added ...

### A better way to explain forcing?

This is an expansion of David Roberts's comment. It may not be the sort of answer you thought you were looking for, but I think it is appropriate, among other reasons because it directly addresses ...
• 65.4k
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### What is the dimension of the mathematical universe?

My co-authors and I introduced a notion of dimension for forcing extensions in the following paper: Hamkins, Joel David; Leibman, George; Löwe, Benedikt, Structural connections between a forcing ...
Accepted

### A better way to explain forcing?

I have proposed such an axiomatization. It is published in Comptes Rendus: Mathématique, which has returned to the Académie des Sciences in 2020 and is now completely open access. Here is a link: ...
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### A better way to explain forcing?

Great Question! Finally someone asks the simplest questions, which almost invariably are the real critical ones (if I cannot explain a great idea to an intelligent person in minutes, it simply means I ...
• 7,683
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### Sheaf-theoretic approach to forcing

Yes, this is a model of ETCSR. Unfortunately, I don't know of a proof of this in the literature, which is in general sadly lacking as regards replacement/collection axioms in topos theory. But here'...
• 65.4k
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### What is the modal logic of outer multiverse?

I've noticed that recently you have asked a few questions about my work, and so let me thank you; you are kind to take an interest. This particular question can be seen as part of the subject of set-...

### Sheaf-theoretic approach to forcing

I think the language of classifying toposes is helpful in understanding this view of forcing. Let $P$ be a poset. The set theorists have the intuition that forcing over $P$ adjoins a generic filter of ...
• 14.9k
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### Why do we need a transitive model in forcing arguments?

Yes, one can undertake forcing without the transitivity assumption, and even the countability of the model is not important. One of the standard ways to do this is with the Boolean-valued model ...
Accepted

### Forcing and Family Contentions: Who wins the disputes?

I like this question a lot. It provides an interesting way of talking about some of the ideas connected with the maximality principle and the modal logic of forcing. Let me make several observations. ...

### A better way to explain forcing?

This answer is quite similar to Rodrigo's but maybe slightly closer to what you want. Suppose $M$ is a countable transitive model of ZFC and $P\in M$. We want to find a process for adding a subset $G$ ...
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### A better way to explain forcing?

I think there are a few things to unpack here. 1. What is the level of commitment from the reader? Are we talking about a casual reader, say someone in number theory, who is just curious about forcing?...
• 37.9k