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.
7
votes
2
answers
297
views
At what ordinal $\chi$ does $\mathrm{L}_\chi$ contain a surjection from $\omega$ to $\mathrm...
Let $\mathrm{ZF^-}$ be $\mathrm{ZF}$ minus power set, and let $\beta_0$ be the ordinal for ramified analysis so that $\mathrm{L}_{\beta_0}$ is the least $\mathrm{L}$-model of $\mathrm{ZF}^-$. Clearly, …
- 3,574
2
votes
1
answer
110
views
Does $\mathrm{L}_{s_{n+1}}$ contain a surjection from $\omega$ to $\mathrm{L}_{s_n}$?
Let $s_n$ be the least $\Sigma_n-$admissible ordinal, so that $\mathrm{L}_{s_n}$ is a model of Kripke-Platek set theory with $\Sigma_n-$collection and $\Sigma_n-$separation.
Does $\mathrm{L}_{s_{n+1}} …
- 20.7k
5
votes
1
answer
340
views
A question on the size of an admissible ordinal
Let $\mathbf{L}_{\varsigma}$ be the level of ordinal $\varsigma$ of Gödel's constructible universe $\mathbf{L}$. Let $\Sigma_{3}$-KP be Kripke-Platek set theory with infinity and $\Sigma_{3}$-$collect …
- 2,031
13
votes
1
answer
2k
views
Are some interesting mathematical statements minimal?
Gödel's set $\mathrm{L}$, of constructible sets, decides many interesting mathematical statements, as the Continuum hypothesis and the Axiom of Choice.
Are some interesting mathematical questions, whi …
- 236k
1
vote
1
answer
248
views
Adjunction, infinity and hereditarily finite sets
Is
$$\mathrm{U}_{\omega}=\Big\{x\mid\forall z\Big(\big(\emptyset\in z\wedge \forall u, v\;(u,v\in z\rightarrow\{w\mid w\in u\vee w=v\}\in z)\big)\rightarrow x\in z\Big)\Big\}$$
identical with the set …
- 3,574
6
votes
4
answers
2k
views
How short can we state the Axiom of Choice?
How short can we state a principle which is equivalent with the Axiom of Choice under $ZF$? The principle should be a sentence in the language of set theory with only $\in$ and$=$ as extralogical rela …
- 4,713
2
votes
1
answer
597
views
"Potency set" for power set?
Cross-posted at HSM.
Has the term "potency set" been used in English language mathematics for power set, and, if so, what are good references?
It is relevant that for historical reasons, "power set" i …
- 12.9k
2
votes
1
answer
379
views
Impredicativity, definition, recursion and conservatism
Suppose we in an impredicative framework isolate the fixed point
$$Gx\leftrightarrow A(G,x)$$
from a $Gx$ obtained by $\Pi^1_1$-comprehension as equivalent to $\forall K((A(K,x)\to Kx)\to Kx)$, where …
- 73.2k
2
votes
1
answer
464
views
First use of corner quotes for Gödel numbers
Who first used the corner quotes, $\ulcorner$ and $\urcorner$, for the notion of Gödel number? They can also be written as\Godelnum with Sam Buss's macro.
They were used by Joseph R. Shoenfield, in Ma …
- 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
-1
votes
1
answer
399
views
Ubiquity beyond infinity, transitive closure and the recursion theorem?
I am considering a Principle of Ubiquity, expressed as follows - for a class theory where precisely the elements are sets - with the aid of set abstracts:
For $\alpha(y,z)$ a first order condition so …
CommunityBot
- 1
2
votes
0
answers
115
views
Will the least class satisfying Scott set theory interpret AC and CH?
I use ST for the set theory used by Dana Scott in More on the Axiom of Extensionality,
in Y. Bar Hillel et alia, Essays on the Foundations of Mathematics}, Hebrew University, Jerusalem: $115-131$. 1 …
- 3,574
6
votes
0
answers
117
views
Ackermann set theory without extensionality?
Scott showed that ZF minus the axiom of regularity is interpreted by ZF minus the axioms of regularity and extensionality.
Is Ackermann set theory interpreted by Akermann set theory without extensiona …
- 3,574
2
votes
0
answers
115
views
Does NBG set theory minus power set minus extensionality interpret NBG set theory minus powe...
In On the Axiom of Extensionality, Part II, JSL, Vol. 24, No. 4, 1959, 287-300, R. O. Gandy shows that NBG set theory minus extensionality interprets NBG set theory. His systems make use of set abstra …
- 3,574
1
vote
0
answers
154
views
Countable $L_\alpha$ model for $S$ if $S$ has a countable well founded model?
Let $S$ be a proper fragment of $\mathit{ZFC}$, and let $S$ properly extend $\mathit{ZFC}^-$, i.e. $\mathit{ZFC}$ minus the power set axiom. Is there a countable ordinal $\alpha$ so that $L_\alpha$ is …
- 3,574