Add to ORKGA field $K$ in a ring language $\mathcal{L}$ is finitely undecidable if $\mbox{Cons}(\Sigma)$ is undecidable for every nonempty finite $\Sigma \subseteq \mbox{Th}(K; \mathcal{L})$. We adapt arguments originating with Cherlin-van den Dries-Macintyre/Ershov (for PAC fields), Haran (for PRC fields), and Efrat (for PpC fields) to prove all PAC, PRC, and (bounded) PpC fields are finitely undecidable. This work is drawn from the author's PhD thesis and is a sequel to arXiv:2210.12729.Comment: 24 page
In this note we give a negative answer to Abraham Robinson’s question of whether a finitely generate...
In this note we give a negative answer to Abraham Robinson’s question of whether a finitely generate...
This thesis is about "decision problems concerning properties of sets of equations". If L is a fi...
It is shown that the compositum Q(2) of all degree 2 extensions of Q has undecidable theory.articl
It is shown that the compositum Q(2) of all degree 2 extensions of Q has undecidable theory.articl
This paper is primarily concerned with the following question which first appeared in Koenigsmannâs ...
This paper is primarily concerned with the following question which first appeared in Koenigsmann’s ...
Fix a prime $p$. We prove that the set of sentences true in all but finitely many finite extensions ...
It is shown that the compositum Q(2) of all degree 2 extensions of Q has undecidable theory.articl
AbstractLet K be a complete and algebraically closed valued field of characteristic 0. We prove that...
Let K, L be finitely generated fields with K ≡ L. Is K isomorphic to L? In 2020, Dittmann and Pop [D...
Let K be an algebraic extension of the rationals and A be the ring of algebraic integers of K. As to...
We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo...
We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo...
We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo...
In this note we give a negative answer to Abraham Robinson’s question of whether a finitely generate...
In this note we give a negative answer to Abraham Robinson’s question of whether a finitely generate...
This thesis is about "decision problems concerning properties of sets of equations". If L is a fi...
It is shown that the compositum Q(2) of all degree 2 extensions of Q has undecidable theory.articl
It is shown that the compositum Q(2) of all degree 2 extensions of Q has undecidable theory.articl
This paper is primarily concerned with the following question which first appeared in Koenigsmannâs ...
This paper is primarily concerned with the following question which first appeared in Koenigsmann’s ...
Fix a prime $p$. We prove that the set of sentences true in all but finitely many finite extensions ...
It is shown that the compositum Q(2) of all degree 2 extensions of Q has undecidable theory.articl
AbstractLet K be a complete and algebraically closed valued field of characteristic 0. We prove that...
Let K, L be finitely generated fields with K ≡ L. Is K isomorphic to L? In 2020, Dittmann and Pop [D...
Let K be an algebraic extension of the rationals and A be the ring of algebraic integers of K. As to...
We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo...
We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo...
We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo...
In this note we give a negative answer to Abraham Robinson’s question of whether a finitely generate...
In this note we give a negative answer to Abraham Robinson’s question of whether a finitely generate...
This thesis is about "decision problems concerning properties of sets of equations". If L is a fi...