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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.

7 votes

Stable theory: question about definability of independece

First, the relation $R(x,y)$ as you defined it is in general not type-definable (although it is definable in any $\aleph_0$-categorical theory, since it is invariant). Indeed, take any stable structu …
Itaï BEN YAACOV's user avatar
3 votes
Accepted

Semigroup product of the left-invariant completion of a Polish group (restatement of Questio...

In the end it was the original question which was answered first. The answer to Is there a relational countable ultra-homogeneous structure whose countable substructures do not have the amalgamation …
Itaï BEN YAACOV's user avatar
5 votes
1 answer
340 views

Semigroup product of the left-invariant completion of a Polish group (restatement of Questio...

This is a re-statement, of sorts, of the question Is there a relational countable ultra-homogeneous structure whose countable substructures do not have the amalgamation property?, so far unanswered. …
Itaï BEN YAACOV's user avatar
16 votes
3 answers
1k views

Is there a relational countable ultra-homogeneous structure whose countable substructures do...

Is there a relational countable ultra-homogeneous structure whose countable substructures do not have the amalgamation property? The question can be stated in a fashion not requiring much backgro …
Itaï BEN YAACOV's user avatar