3.122 lo.logic questions.

7 Interpreting a space in Baire space: how many facts do I need to understand the whole thing?

Below I'm working in ZF+DC+AD or similar; I want enough choice that things don't explode, but I also want the Wadge hierarchy to be well-behaved everywhere. Since this question is a bit long, I've put ...

-5 Is transcendental Goldbach Conjecture true of the real numbers?

Let $x0$ be the real number $Pi$, Consider the below sequence of real numbers: $s{0}$ = .1415926535897932384626433832795028841971... $s{1}$ = .415926535897932384626433832795028841971... $s{2}$ = ....

2 If any satisfiable $\mathcal{L}_{κ,κ}(Q_{=κ})$-theory remains satisfiable when replacing $Q_{=κ}$ with $Q_{=μ}$, is $κ$ huge?

Recently, I have asked a model-theoretic question concerning a weakening of different forms of compactness. I now present another model-theoretic question as a weakening of hugeness. If any ...

6 Are there logical systems where formal proofs are not computer verifiable?

3 answers, 736 views lo.logic computer-science foundations
In a set-theoretic system using first-order logic, every proof could be written as a goal followed by a finite sequence of sentence where each one is justified by an axiom or previously established ...

3 A definition of the generic real coded by a generic filter?

3 answers, 286 views set-theory lo.logic
Apologies if this question is a bit simplistic/vague for MO: I'm looking for an all-purpose definition in the literature of when a sufficiently generic filter "canonically codes" a generic real. ...

10 Is being close to a Halting set computable?

2 answers, 619 views lo.logic computability-theory
Let $\Phi$ be a universal Turing machine and let $S$ be the set on which it halts. I’m curious about if its decidable to check if a number is close to $S$. There are two notions of distance that come ...

7 How much can complexities of bases of a “simple” space vary?

Given a countable subbase of a topology, we can consider its complexity in terms of the difficulty of determining whether one family of basic open sets covers another basic open set. My question is ...

13 Is it ever a good idea to use Keisler-Shelah to show elementary equivalence?

4 answers, 1.364 views lo.logic set-theory model-theory ultrapowers
The most useful way I know to show that two structures are elementarily equivalent is Ehrenfeucht-Fraisse games. These are quite nice and intuitive, and even when I can't use them to solve my problem ...

14 What does it mean to 'discharge assumptions or premises'?

4 answers, 6.645 views lo.logic proof-theory
When constructing proofs using natural deduction what does it mean to say that an assumption or premise is discharged? In what circumstances would I want to, or need to, use such a mechanism? The ...

2 relatively free groups in $Var(S_3)$

Suppose $S_3$ is the symmetric group of order 6. Which elements of the variety $Var(S_3)$ are relatively free? This question is related to my previous question Relatively free algebras in a variety ...

15 $GCH$ and special Aronszajn trees

2 answers, 755 views lo.logic set-theory gch
Question. Does $\text{GCH}$ imply the existence of a non-special $\aleph_2$-Aronszajn tree ? Remark 1. By a result of Jensen, it is consistent that $\text{GCH}$ holds and all $\aleph_1$-Aronszajn ...

2 Formal definition of this ordinal?

1 answers, 259 views lo.logic ordinal-numbers

30 What is the status of the Hilbert 6th problem?

As you know, the Hilbert sixth problem was to axiomatize physics. According to the Wikipedia article, there is some partial succes in this field. For example, Classical mechanics, I believe, can be ...

1 Looking for help in defining a new epistemic logic

0 answers, 61 views lo.logic model-theory modal-logic
I'm looking for some guidance in defining a new epistemic, temporal logic. I am looking to extend a logic called Sequential Epistemic Logic (SPAL): https://pdfs.semanticscholar.org/dae6/...

1 Proof of the Specker-Blatter theorem

0 answers, 119 views lo.logic model-theory

Probabilistic generalization of trial-and-error predicates

1 answers, 51 views lo.logic computability-theory
The notion of a limiting recursive set (Gold 1965, J. Symb. Log. 30: 28–48) or trial and error predicate (Putnam 1965, J. Symb. Log. 30: 49–57) is defined as follows. A guessing function is a total ...

9 What is the consistency strength of weak Vopenka's principle?

Weak Vopěnka's principle says that the opposite of the category of ordinals cannot be fully embedded in any locally presentable category. Recall that one form of Vopěnka's principle says that the ...