Marcus Tressl
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View article: Subfitness in distributive (semi)lattices
Subfitness in distributive (semi)lattices Open
We investigate whether the set of subfit elements of a distributive semilattice is an ideal. This question was raised by the second author at the BLAST conference in 2022. We show that in general it has a negative solution, however if the …
View article: A model theoretic perspective on matrix rings
A model theoretic perspective on matrix rings Open
In this paper natural necessary and sufficient conditions for quantifier elimination of matrix rings $$M_n(K)$$ in the language of rings expanded by two unary functions, naming the trace and transposition, are identified. This is …
View article: On ordinary differentially large fields
On ordinary differentially large fields Open
We provide a characterization of differentially large fields in arbitrary characteristic and a single derivation in the spirit of Blum axioms for differentially closed fields. In the case of characteristic zero, we use these axioms to char…
View article: Differentially large fields
Differentially large fields Open
We introduce the notion of differential largeness for fields equipped with\nseveral commuting derivations (as an analogue to largeness of fields). We lay\nout the foundations of this new class of "tame" differential fields. We state\nsever…
View article: On ordinary differentially large fields
On ordinary differentially large fields Open
We provide a characterisation of differentially large fields in arbitrary characteristic and a single derivation in the spirit of Blum axioms for differentially closed fields. In the case of characteristic zero, we use these axioms to char…
View article: Differential Weil descent
Differential Weil descent Open
In this short note a differential version of the classical Weil descent is established in all characteristics. This yields a ready-to-deploy tool of differential restriction of scalars for differential varieties over finite differential fi…
View article: Differentially Large Fields
Differentially Large Fields Open
We introduce the notion of differential largeness for fields equipped with several commuting derivations (as an analogue to largeness of fields). We lay out the foundations of this new class of "tame" differential fields. We state several …
View article: Defining integer valued functions in rings of continuous definable functions over a topological field
Defining integer valued functions in rings of continuous definable functions over a topological field Open
Let K be an expansion of either an ordered field or a valued field. Given a definable set X $\subseteq$ Km let C(X) be the ring of continuous definable functions from X to K. Under very mild assumptions on the geometry of X and on the stru…
View article: A Model Theoretic Perspective on Matrix Rings
A Model Theoretic Perspective on Matrix Rings Open
In this paper natural necessary and sufficient conditions for quantifier elimination of matrix rings $M_n(K)$ in the language of rings expanded by two unary functions, naming the trace and transposition, are identified. This is used togeth…
View article: Differential Weil Descent and Differentially Large Fields
Differential Weil Descent and Differentially Large Fields Open
A differential version of the classical Weil descent is established in all characteristics. It yields a theory of differential restriction of scalars for differential varieties over finite differential field extensions. This theory is then…
View article: On the strength of some topological lattices
On the strength of some topological lattices Open
We study the model theoretic strength of various lattices that occur\nnaturally in topology, like closed (semi-linear or semi-algebraic or convex)\nsets. The method is based on weak monadic second order logic and sharpens\nprevious results…
View article: Interpreting formulas of divisible lattice ordered abelian groups
Interpreting formulas of divisible lattice ordered abelian groups Open
We show that a large class of divisible abelian $\ell$-groups (lattice ordered groups) of continuous functions is interpretable (in a certain sense) in the lattice of the zero sets of these functions. This has various applications to the m…
View article: On the strength of some topological lattices
On the strength of some topological lattices Open
We study the model theoretic strength of various lattices that occur naturally in topology, like closed (semi-linear or semi-algebraic or convex) sets. The method is based on weak monadic second order logic and sharpens previous results by…