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 37385
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.
0
votes
1
answer
295
views
Weak Skolem-Löwenheim and completeness
In T. Skolem 1922 the author publishes a weak version of the Skolem-Löwenheim theorem which we call WLS and which according to Wikipedia says that every countable theory which is satisfiable in a mode …
- 3,574
4
votes
1
answer
221
views
May open sentences be eliminated?
Saul Kripke famously invoked a free logic to avoid validating the Barcan Formula and its converse. In that context he adduced a generality interpretation of free variables. The converse of the Barcan …
- 3,574
0
votes
1
answer
119
views
How may a largest fixed-point be defined in second order logic?
Adapting from Anil Gupta and & Nuel Belnap, Revision theory of truth, MIT 1993, p. 194, in the context of a second order logic, where $A(x.G)$ is a formula where $G$ only occurs positively, a fixed po …
- 3,574
1
vote
0
answers
65
views
Algebraization of arithmetic and stronger theories?
Intuitionistic and classical propositional logic, and even classical first-order logic with identity, have algebraic counterparts. Algebraizable logics, 1989, by Willem J. Blok and Don Pigozzi, is a c …
- 3,574
1
vote
0
answers
172
views
May we axiomatize by means of Gödel codes?
Suppose we have a classical arithmetical theory $\mathbf{R}$, at least as strong as Robinson arithmetic, with $\tau$ an extra dummy monadic predicate in its language $\mathcal{L}$. Suppose $\mathbf{R} …
- 3,574
3
votes
1
answer
246
views
Representing modus ponens in a Polish propositional logic with NAND as the only connective
In a base for propositional logic using the Polish connective $\uparrow$ for not both, J. Nicod isolated one axiom as sufficient:
$\uparrow\uparrow p\uparrow q r\uparrow\uparrow t\uparrow tt\uparrow\ …
- 3,574
1
vote
0
answers
106
views
A question on complexity notation
I am considering writing ''$\Pi^{n}_{i_{0},...,i_{n-1}}$-comprehension'' as abbreviation for ''$\Pi^{0}_{i_{0}}$-comprehension plus ... plus $\Pi^{n-1}_{i_{n-1}}$-comprehension'' in the context of an …
- 3,574
1
vote
0
answers
96
views
Is Jaskowski's paraconsistent system moderate if sparked?
Stanislaw Jaskowski published a non-adjunctive paraconsistent logic, which does not have the inference rule $\vdash A \ \& \ \vdash B\Rightarrow \ \vdash A\wedge B$. The paper first appeared in Poli …
- 3,574
2
votes
1
answer
213
views
A question on the name of a property
What is the name of the following property of a system $T$?
If $\vdash_{T}\exists x F(x)$ then
there is a term $a$ such that $\vdash_{T} F(a)$
If I recall correctly Heyting Arithmetics has …
- 3,574
2
votes
1
answer
180
views
What are the adequacy conditions for Rosser Provability?
Famously, Rosser introduced a provability predicate $\pi[A]$ that holds iff $\exists x(xP[A]\wedge\forall y(y\le x\to\lnot yP[\lnot A]))$.
Supposing $PA$ is consistent, what are the adequacy conditio …
- 3,574
6
votes
1
answer
189
views
Does $WKL_0$ provide more comprehension than $RCA_0$?
$WKL_0$ extends $RCA_0$ with the statement that any infinite subset of the infinite binary tree has an infinite branch. Does $WKL_0$ Prove that there are sets which are not proven to exist by the $\De …
- 3,574
4
votes
2
answers
212
views
What can be achieved by liberalizing induction for $RCA_0$?
$RCA_0$ has $\Delta_0$-comprehension and $\Sigma_1$ induction. Let $X\Sigma_{n}$ be $RCA_0$ plus $\Sigma_n$-induction and let $X\Sigma_{\omega}$-induction be $RCA_0$ plus the full induction schema.
…
- 3,574
2
votes
1
answer
270
views
Is Extensionality needed for the incompleteness of very weak set theories?
$ST$ is the weak set theory built upon identity theory and containing
the axiom for empty set,
the axiom for adjunction and
the axiom for extensionality.
It is known that $ST$ interprets Robin …
- 3,574
2
votes
0
answers
119
views
A Question on Provability Logic and Co-Necessitation
The provability logic $GL$ has the characteristic axioms:
$K\hspace{15pt}\Box(\alpha\rightarrow \beta)\rightarrow(\Box\alpha\rightarrow\Box\beta)$
$L\hspace{15pt}\Box(\Box \alpha\rightarrow \alpha) …
- 3,574
2
votes
0
answers
408
views
A question on the consistency of a (seemingly) very weak set theory
I have preoccupied myself some with very weak set theories that suffice to interpret Robinson Arithmetic, as in this question Is Extensionality needed for the incompleteness of very weak set theories? …
- 3,574