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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.

0 votes
1 answer
184 views

Combinatorially defined effectively closed set

Is there a combinatorially defined, nonempty effectively closed set $Q\subseteq 2^\omega$ such that all members of $Q$ are incomputable? Combinatorially defined means that the definition of $Q$ does …
Jiayi Liu's user avatar
  • 909
6 votes
1 answer
193 views

Complexity of a combinatorial constraint

For two $k$-partitions $X,Y\in k^\omega$ of $\omega$ (seen as functions $\omega\rightarrow k$), we say $X,Y$ are almost disjoint iff $X^{-1}(i)\cap Y^{-1}(i)$ is finite for all $i<k$. Question: Does …
Jiayi Liu's user avatar
  • 909
8 votes
2 answers
484 views

Comprehension axiom that helps in the opposite direction

Usually, having more comprehension axiom means the more you can prove. We wonder if the converse can be the case. Is there a natural problem $\mathsf{P}$ so that $\mathsf{P}+\neg(\Gamma-\mathsf{Compre …
Jiayi Liu's user avatar
  • 909