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 not deleted
user 11145
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.
10
votes
2
answers
386
views
Iteration of $\aleph_2$-properness
Let us say a forcing $P$ is proper for a class of models $\mathcal C$, if for large enough regular $\theta$ and $M \prec H_\theta$ in $\mathcal C$ with $P \in M$, every $p \in P \cap M$ can be extende …
- 1,291
9
votes
0
answers
162
views
Algebraic structures on spaces of ultrafilters
The space of ultrafilters on $\omega$ has a natural semigroup structure, and ultrafilters that are idempotent in that algebra have seen applications in combinatorics on the natural numbers, for exampl …
- 18.7k
3
votes
Accepted
Is discriminative choice provable in ZFC?
Yes. Enumerate $F$ as $\langle F_\alpha : \alpha<\kappa\rangle$, where $\kappa$ is a cardinal. Inductively pick $x_\alpha \in F_\alpha$ such that $x_\alpha$ is not $\phi$-equivalent to any $x_\beta$, …
- 18.7k
6
votes
A reference for forcing projections
I don’t know if there’s a “canonical” writeup, but I taught a master’s course a few years ago and wrote up many details of these things here. But maybe this isn’t useful if you’re looking for somethi …
- 18.7k
13
votes
Truth in a different universe of sets?
In contrast to Joel's answer, I would like to point out that the notion of truth-in-a-structure, or whether $A \models \phi$ for a given $A,\phi$, is not so wild and capricious. Although the question …
- 18.7k
17
votes
6
answers
1k
views
Strategic vs. tactical closure
The Banach-Mazur game on a poset $\mathbb P$ is the $\omega$-length game where the players alternate choosing a descending sequence $a_0 \geq b_0 \geq a_1 \geq b_1 \geq \dots$. Player II wins when th …
- 2,163
3
votes
2
answers
339
views
Ultrafilter projections and critical points of factor maps
Suppose $j : V \to M$ is $\lambda$-supercompactness embedding derived from an $\kappa$-complete normal ultrafilter $U$ on $P_\kappa(\lambda)$, $\lambda$ regular. Suppose $\eta$ is an ordinal such tha …
- 8,099
4
votes
Existence of trees with height $\omega$, size $\aleph_1$ and $\aleph_2$ maximal branches
Suppose $T$ is a tree of height $\omega$ with $<2^\omega$-many branches. Then it must be the case that for all $t \in T$, there is $s \geq t$ such that all $x \geq s$ are comparable. Otherwise we co …
- 18.7k
9
votes
1
answer
417
views
Natural set-theoretic principles implying the Ground Axiom
The Ground Axiom states that the set-theoretic universe is not a set-forcing extension of an inner model. By
Reitz, it is first-order expressible and easy to force over any given ZFC model with class …
- 12.9k
7
votes
0
answers
183
views
Interest in the size of ultrapowers in model theory
It seems that in the 60s (at least), there was interest in computing the size of ultrapowers by countably incomplete ultrafilters. For example, given an ultrafilter $U$ on some relatively small set l …
- 18.7k
5
votes
1
answer
154
views
Countable closure of quotient forcing
Let us say that a partial order is "countably closed with infima" if every descending $\omega$-sequence has an infimum.
Suppose $P$ and $Q$ are posets that are countably closed with infima, and for so …
- 2,163
1
vote
closure of separative quotients
If $P$ is a non-atomic poset that is $\kappa$-closed forces that $|P|=\kappa$, then the separative quotient of $P$ is equivalent to $\mathrm{Col}(\kappa,|P|)$. This can be shown using the folklore ar …
- 18.7k
13
votes
2
answers
593
views
Amoeba collapse
Here is a naive idea for a forcing $\mathbb A(\kappa)$, for an inaccessible cardinal $\kappa$. Conditions are pairs $(P,p)$, where $P \in V_\kappa$ is a partial order and $p \in P$. We define the or …
- 2,163
8
votes
Accepted
Amoeba collapse
$\kappa$ is preserved, and moreover all reals are added by the small generics.
Let $(P_0,p_0)$ be a condition and let $\sigma$ be a name for a real. First, enumerate the elements of $P_0$ below $p_0$ …
- 18.7k
13
votes
1
answer
557
views
Iterating Neeman's forcing
In the paper, "Forcing with sequences of models of two types," (MR3201836), Neeman claims that, using a supercompact and a weakly compact above, one can force with his pure side conditions poset twice …
- 18.7k