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Results tagged with lo.logic
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user 103802
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.
11
votes
Forcing notions adding minimal reals
Splitting forcing is a little-known forcing that adds a splitting real and creates a minimal extension. It consists of splitting trees ordered by inclusion. A splitting tree is a perfect tree $T \subs …
5
votes
Independent families on $\omega$ with an additional splitting property
Edit: My previous answer had a mistake. Here is an updated answer which still contains some hopefully useful information:
Assuming $\operatorname{cov}(\mathcal{M}) = \mathfrak{d}$, there is a positive …
2
votes
Independent families of functions on $\omega$ of size continuum
For (d) maybe the following was meant:
Take your independent family $F$ and partition it into continuum many families of size $\omega$:
$F = \{ I_{\alpha,n} : \alpha< \mathfrak{c},n \in \omega \}$ …