Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with lo.logic
Search options answers only
not deleted
user 2000
first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
3
votes
Accepted
Are Cohen Generics Minimal Covers?
Indeed, this has been answered very negatively in the literature:
Abraham, Uri; Shore, Richard A., The degrees of constructibility of Cohen reals, Proc. Lond. Math. Soc., III. Ser. 53, 193-208 (1986). …
- 44.4k
41
votes
Who needs Replacement anyway?
I think the main reason replacement is seen as an essential part of ZF is that it naturally follows from the ontology of set theory, as do the other axioms of ZF. The ontology of set theory is rooted …
- 4,713
3
votes
Am I doing a forcing argument here?
It looks like the "logic aspects" of the argument boil down to using compactness. [However, this appears to be moot since the argument may have flaws pointed out by Will Sawin.]
First, given a bound …
- 44.4k
0
votes
When can a function defined on $[a, b] \cup [b, c]$ be constructively extended to a function...
This is mostly a long comment, not really an answer.
If one slightly modifies the closed interval notation as follows:
$$[a,b\Vert = \{ x : a \leq x \not\gt b \}$$
$$\Vert b,c] = \{ x : b \not\gt x \l …
- 44.4k
6
votes
Is the Ordering Principle equivalent to a selection principle?
Here is a variation on the same theme as Joel David Hamkins' answer.
Theorem. The following are equivalent over ZF set theory:
Every set admits a linear order.
For every set $X$, there is a function …
- 44.4k
39
votes
Most 'unintuitive' application of the Axiom of Choice?
I highly recommend reading this paper by Chris Hardin and Al Taylor, A Peculiar Connection Between the Axiom of Choice and Predicting the Future (Wayback Machine), as well as this shorter piece by Mik …
- 4,713
7
votes
Accepted
Formulas that are valid simultaneously in a power set Boolean algebra $B$ and the 2-element ...
The class of formulas you're looking for contains all quasi-identities:
$$a_1 = b_1 \land \cdots \land a_k = b_k \to a = b$$
where $k \geq 0$ and $a,a_1,\ldots,a_k,b,b_1,\ldots,b_k$ are terms formed u …
- 44.4k
14
votes
About the axiom of choice, the fundamental theorem of algebra, and real numbers
Regarding Cauchy and Dedekind reals. The fact that every Dedekind real has a Cauchy representation is provable in very weak systems of intuitionistic analysis. The converse fact that every Cauchy real …
- 4,713
33
votes
Accepted
Does $\operatorname{Con}\sf(ZF)$ imply $\operatorname{Con}\sf(ZF + \operatorname{Aut}{\bf C ...
The use of inaccessible cardinals is not necessary here, the Baire property works just as well as Lebesgue measure. Shelah (Can you take Solovay's inaccessible away, Isr. J. Math. 48, 1984, 1-47) show …
- 39
29
votes
Are $\mathbb{C}$ and $\overline{\mathbb{Q}}_p$ isomorphic?
First, let me observe that it is consistent with $\mathsf{ZF}$ + $\mathsf{DC}$ that there is no such isomorphism. (This follows from this answer of mine.) However, as I commented on Torsten's post, th …
- 39
6
votes
Accepted
Comparing bornologies for domination/escaping
Note that $\mathfrak{b}=\mathfrak{d}$ is equivalent to the existence of a $<^\ast$-increasing sequence $(f_\alpha)_{\alpha<\mathfrak{d}}$ which is cofinal in $(\mathcal{N},{<^\ast})$, where $f <^\ast …
- 44.4k
8
votes
Accepted
Are we sure the calculus of inductive constructions and ZFC plus countably many inaccessible...
The situation is a bit subtle. One can interpret CIC in any model of ZFC with infinitely many inacessibles. However, interpreting ZFC in CIC is more subtle. First one needs to assume the law of exclud …
- 44.4k
8
votes
How much induction does a p-adic valuation need?
This is not intended as an answer but rather as a long-winded explanation of what having a 2-adic valuation means for really weak theories such as Q and open induction, which is much too long for a co …
- 44.4k
4
votes
When is $A$ "$L$-ish" whenever $B$ is "$L$-ish"?
Here is an extension of Barwise's theorem which may be of some use.
Theorem. Fix a real $a \subseteq \omega$ in $W$. Suppose the preorder $\preceq$ is first-order definable with parameter $a$ and that …
- 20.7k
6
votes
Accepted
The strength of "There are no $\Pi^1_1$-pseudofinite sets"
My "hunch" in the comments to the question appears to be correct! This model comes from Howard, Paul E.; Yorke, Mary F., Definitions of finite, Fundam. Math. 133, No. 3, 169-177 (1989). ZBL0704.03033. …
- 44.4k