All Questions

As is known, Tarski posed his questions about first-order theories of non-abelian free groups around 1945. However, the questions were not published in his papers or books. What is the original ...

Is there a way to axiomatize [non-abelian] free groups in first-order logic using the language of groups (which contains the binary operation symbol $\cdot$, and the constant symbol $e$)? Is there ...

Let $w$ be a word in a free group $F_2$ of two generators $x_1, x_2$ such that there does not exist any endomorphism of free group which takes $w$ to $w^{-1}$. Let $w_1, w_2$ be two words in the same ...

Let $G$ be a fully residually free group with a finitely generated profinite completion. Is $G$ necessarily finitely generated?