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Results tagged with lo.logic
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user 57114
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
Function $f:\kappa\to\alpha$ with small fibers where $\alpha\in\kappa$
Yes, this is consistent.
Consider a (transitive) model of $\mathrm{ZF}$ in which $\omega_1$ has countable cofinality. Fix a strictly increasing, cofinal sequence $(\xi_n \mid n < \omega)$ in $\omega …
- 1,080
4
votes
2
answers
405
views
The $\delta$-approximation property for ground models
Definition 1 (Hamkins).
Suppose $V \subseteq W$ are transitive models of $\mathrm{ZFC}$ and $\delta$ is a cardinal in $W$.
$(V,W)$ has the $\delta$-cover property iff for each
$A \in W$ with $A \s …
- 1,080
3
votes
Regarding extenders
Fix $(a_n \mid n < \omega)$, $(x_n \mid n < \omega)$ such that $x_n \in E_{a_n}$ for all $n < \omega$. Without loss of generality we may assume
$\{\xi\} \in \{a_n \mid n < \omega \}$ for all $\xi \i …
- 1,080
4
votes
0
answers
201
views
Equivalent definitions of Woodin cardinals in $\operatorname{ZFC}_{-}/\operatorname{ZFC}^{-}$
In our background universe $V$ - satisfying $\operatorname{ZFC}$ - we say that an ordinal $\delta$ is a Woodin cardinal iff it satisfies one of the following equivalent properties:
For all $A \subse …
- 1,080
5
votes
1
answer
341
views
What is a 'power admissible model'?
Q: What exactly is a power admissible model?
Background: Admissible models, introduced by Jon Barwise, form the building blocks of inner model theory. They are transitive models $\mathcal M = (M; \in …
- 1,080
6
votes
0
answers
242
views
Does $0^{\#}$ imply that $L$'s set generic multiverse has irreconcilable theories?
Suppose $0^{\#}$ exists. Let $M(L)$ be the generic multiverse over $L$ as viewed in $V$, i.e. $M(L)$ consists of all $L[g]$ where $g \in V$ is $\mathbb{P}$-generic over $L$ for some forcing $\mathbb{P …
- 1,080
2
votes
Accepted
Mitchell, Steel. FSIT. Lemma 2.8: Is $k$-solidity actually needed?
In my question I already verified that (assuming 1. and 2.) item 3. is provable without assuming that $\pi(r)$ is $k$-solid over $(\mathcal{M},q)$. To see that we can actually drop $k$-solidity in thi …
- 1,080
4
votes
1
answer
241
views
Mitchell, Steel. FSIT. Lemma 2.8: Is $k$-solidity actually needed?
Consider the following result (which is Lemma 2.8 in Mitchell and Steel's paper on Fine Structure and Iteration Trees):
Lemma 2.8 Let $\pi \colon \mathcal{H} \to \mathcal{M}$ be generalized $r \Sigma …
- 1,080