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Results tagged with lo.logic
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user 134910
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
Internal vs. external definability of inner models
I will try to partially answer your question. I claim that if $\kappa$ is weakly compact then this situation is inconsistent: I will show that such an $M$ is necessarily definable in $V_\kappa$.
Defi …
- 1,291
6
votes
Accepted
Formal proof of $ZFC \vdash CON(\ulcorner ZFC-P\urcorner)$
You can directly show from $ZFC$ that $\forall n \in X_{ZFC-P}\, \colon \, ( H(\omega_1) \vDash n)$. To see this remind yourself that $ \vDash$ is expressible by a single formula $\psi$, so that $H(\ …
- 1,291
10
votes
$\omega_1$-approximation property for Sacks iteration— contradiction in literature?
Exactly. The rumour (not folklore ;) ) is even wrong if you iterate Cohen forcing (on $\omega$ !!) with countable support $\omega_1$ many times. Let $P$ denote the iteration of Cohen forcings. It foll …
- 1,291
3
votes
Accepted
Complexity of a combinatorial constraint
The answer is yes for $r=3$. Take an ultrafilter $\mathcal{U}$ on $\omega$. Define a function $f \colon 3^\omega \rightarrow 3$ such that $f(X):=i$ iff $X^{-1}(i) \in \mathcal{U}$. Note that if $X_1$ …
- 1,291
9
votes
Accepted
Iteration of $\aleph_2$-properness
In https://arxiv.org/pdf/1808.01636 Rosłanowski defines for every $\kappa$ which satisfies $\kappa^{{<}\kappa} = \kappa$ a ${<}\kappa$-closed, $\kappa^+$-c.c. forcing notion whose full support $\omega …
- 1,291