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 6794
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.
5
votes
Accepted
A question about sentences undecidable in Peano's Arithmetic
Since you're asking about provability in SOA, you're presumably referring to a standard deduction system, such as the one in Steve Simpson's book, which is sound not only for the standard (or "full") …
- 73.2k
8
votes
In which sense "closure" is a closure?
A formula is called open if it has free variables. The reason for that name is that such a formula doesn't get a truth value as soon as you specify a structure; you have to also specify values for th …
- 73.2k
4
votes
How to ensure a clean conservative extension in general?
The first of your two constructs doesn't seem to keep things clean in the sense that you described. Suppose, for example, that $L$ is primitive recursive arithmetic, formulated in a way that allows o …
- 73.2k
5
votes
Heyting's Intuitionist PC
The usual intuitionistic implication, for example in Heyting's predicate calculus, should be considered an intuitionistic analog of classical material implication, not of any modal or relevantist noti …
- 73.2k
8
votes
Accepted
Question about Godel's Proof book (Ernest Nagel / James R. Newman)
I don't have the book in front of me right now, so the following may not exactly match what it says, but it should be close enough to give you the right idea. The function sub is defined so that, if …
- 73.2k
2
votes
Accepted
Real closed fields in HOD
The new question added a few minutes ago can be answered by the same idea as in Emil's comment. The following paragraph is provable in ZFC and therefore true in HOD:
For any cardinal $\kappa\leq\mat …
- 73.2k
3
votes
Admissible sets and infinitary languages
I suspect you didn't mean literally what you asked, but if you did, then the answer is yes. You required only that $X$ be a subset of $\mathcal A$, so even if $X$ consists entirely of finitary sentenc …
- 73.2k
4
votes
Accepted
A question about first order theories having only finite models.
Yes. Any sentence in the language of the theory is either true in all models or false in all models, since all models are isomorphic. By the completeness theorem, each sentence is either provable or …
- 73.2k
28
votes
Accepted
Unprovable statements S where the only way to prove S is to assume S
The following is essentially Joel's answer and also essentially the last part of Francois's answer, but its "look and feel" seems different enough to make it worth pointing out. The main point is tha …
- 73.2k
7
votes
About some functions in the set of the natural numbers
Suppose, toward a contradiction, that $f$ is definable in Presburger arithmetic. By quantifier elimination for Presburger arithmetic, there must be a constant $M$ such that, on each congruence class …
- 73.2k
4
votes
Accepted
Reflection principles
I suppose the "paradox" you're asking about is the passage marked with >> at the link you gave, but with "$\omega$-model" in place of "model" and with "has an $\omega$-model" in place of "is consisten …
- 73.2k
3
votes
term equality in algebraic theories
Whether a particular equation is a consequence of other given equations won't depend on the logic, as long as the logic stays within reasonable bounds. The lower bound is that the logic should includ …
- 73.2k
14
votes
Accepted
Predicative definition
A definition of an object X is called impredicative if it quantifies over a collection Y to which X itself belongs (or at least could belong). The classic example is the set occurring in Russell's pa …
- 73.2k
4
votes
Accepted
How to reconcile Godel's theorem with the completeness of the Predicate Calculus?
A model of arithmetic in which the G"odel sentence "I am unprovable" is false is necessarily a non-standard model. It contains an infinite element which satisfies, in the model, the formula expressin …
- 73.2k
6
votes
Accepted
Generalization of the club filter
Here's a little piece of an answer: Section 3 of Solovay's paper "The independence of DC from AD" (Cabal Seminar 76-77, Springer Lecture Notes in Math 689 (1978) pp. 171-183) has a construction of a n …
- 73.2k