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Results tagged with set-theory
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user 109561
forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
3
votes
1
answer
293
views
Forcing CH but not adding $\omega_1$-sequences
Given a ctm $M$, is there a forcing which does not add $\omega_1$-sequences, and forces CH in $M[G]$?
- 79
4
votes
2
answers
187
views
(When) is the range of a bijection $f\in M[G]$ in the ground model $M$?
Let $M$ be a countable transitive model of ZF-P, $\mathbb P$ the set of injections from a countable subset of $\mathbb R$ into $\omega_1$ with $\le=\supseteq$. Let $G$ be a $\mathbb P^M$-generic filte …
- 79