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Results tagged with lo.logic
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user 138274
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
Accepted
Thick Canadian trees
$\newcommand{\Add}{\operatorname{Add}}$Start with a model $V$ satisfying $GCH$ (or just $2^{\omega}=\omega_1$ and $2^{\omega_1}=\omega_2$). Force over $V$ with the product $\Add(\omega,\omega_2)\times …
- 1,799
1
vote
Can Friedman's property fail at or above a supercompact cardinal?
This is more of a long comment. In Harvey Friedman's original paper introducing the property (called "On closed sets of ordinals"), he mentions at the end that, if $M[G]$ is obtained by forcing with $ …
- 1,799
6
votes
1
answer
292
views
Are the following two "tree properties" equivalent?
Let $\kappa$ and $\lambda$ be cardinals. A thin $(\kappa,\lambda)$-list is a function $L:[\lambda]^{<\kappa}\longrightarrow [\lambda]^{<\kappa}$ such that for all $x\in[\lambda]^{<\kappa}$, $L(x)\subs …
- 1,799
3
votes
Stationary many subsets of $\kappa^+$ whose order type is a cardinal and whose intersection ...
I hope revisiting an old question is not frowned upon, but i think i have been able to improve both the lower and the upper bound of the consistency strength:
For the lower bound, Lemma 38.11 in Jech …
- 1,799
20
votes
Accepted
Changing the cofinality of a regular cardinal without collapsing any cardinals?
The possibility of changing the cofinality of a regular cardinal without collapsing any cardinals is equiconsistent with a measurable cardinal:
On one hand, if $\kappa$ is measurable, then by Prikry F …
- 1,799