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 questions only
not deleted
user 3199
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.
4
votes
3
answers
373
views
Official names for specific compound sentences
This question is, admittedly, a little less mathematical than what I normal ask. I seemed to remember that the compound sentence $A\wedge \neg A$ has an official name (maybe even "contradiction" but …
- 18.7k
22
votes
5
answers
2k
views
Platonic Truth and 1st Order Predicate Logic
Consider the following simple example as motivation for my question. If it were the case that, say, the Riemann hypothesis turned out to be independent of ZFC, I have no doubt it would be accepted by …
- 18.7k
2
votes
2
answers
474
views
Platonic Truth and 1st Order Logic - Take 2
As an algebraist, I have some strong intuitions about what it means for an algebraic result to be true. In particular, my intuition would lead me to believe that if I cannot construct a counter-examp …
- 18.7k
17
votes
0
answers
536
views
Are there more true statements than false ones?
It is a nontrivial fact that half the primes are $\equiv 1 \pmod{4}$ and the other half are $\equiv 3\pmod{4}$. The Chebyshev bias suggests, however, that the latter class of primes is winning the ra …
- 18.7k
32
votes
6
answers
5k
views
How do we recognize an integer inside the rationals?
My question is fairly simple, and may at first glance seem a bit silly, but stick with me. If we are given the rationals, and we pick an element, how do we recognize whether or not what we picked is …
- 18.7k
4
votes
3
answers
499
views
Defining negation
I'm currently coauthoring a book intended to teach first-year students basic proof techniques. One of the chapters, written by my coauthor, is about basic logic. In that chapter the negation of a st …
- 18.7k
11
votes
2
answers
933
views
Set theory bootstrapping
Let $\mathcal{L}$ be the first order language of ZFC set theory, and let $\mathcal{L}_{\infty,\infty}$ be the usual infinitary extension of the language allowing arbitrary long disjunctions/conjunctio …
- 18.7k
2
votes
0
answers
233
views
Representing iteration of a function in PA
Let $\mathscr{L}$ be a (recursive) FOL language, with numeral symbols $\underline{0},\underline{1},\ldots$. Let $T$ be a recursive, consistent theory, containing PA (or even just Robinson arithmetic) …
- 18.7k
1
vote
0
answers
126
views
Minimizing all aspects of the definition of Boolean algebra
There are many equivalent ways to describe Boolean algebras. There are a number of different ways to "minimize" the description. We can:
Minimize the number of function symbols.
Minimize the arity …
- 18.7k
8
votes
3
answers
820
views
Does a left basis imply a right basis, without AC?
If $_DV_D$ is a $D$-$D$-bimodule, and we have a $D$-basis for $V_D$, do we still need AC to get a $D$-basis for $_DV$?
(The original question appears below. But this shorter question gets at the hea …
- 18.7k
11
votes
4
answers
2k
views
When is it okay to intersect infinite families of proper classes?
For experts who work in ZFC, it is common knowledge that one cannot in general define a countable intersection/union of proper classes. However, in my work as a ring theorist I intersect infinite col …
- 18.7k
29
votes
10
answers
4k
views
Defining the standard model of PA so that a space alien could understand
First, some context. In one of the comments to an answer to the recent question Why not adopt the constructibility axiom V=L? I was directed to some papers of Nik Weaver at this link, on conceptualis …
- 18.7k
14
votes
3
answers
2k
views
Tarski's truth theorem — semantic or syntactic?
I was reading the sketch of the proof of Tarski's theorem in Jech's "Set Theory", which appears as Theorem 12.7, thinking that it would be an interesting result to really understand. As stated in the …
- 18.7k
17
votes
1
answer
2k
views
The axiom of choice as a consequence of a stronger semantics?
I've never had a problem with the axiom of choice, but it has often confused me how many authors find full choice so much different from finite choice. In my head they seem quite similar. We are pic …
- 18.7k
24
votes
2
answers
1k
views
What do you do if you believe a problem is undecidable?
While the title of this question is subjective, I hope to make what I'm looking for quite concrete. The first, and main question is this: If you believe that a problem you are working on is formally …
- 18.7k