We call finitely generating an inference rule in a sequent system [7] if, given its conclusion, there is only a finite set of premises to choose from. This property is desirable from the viewpoint of proof search, since it implies that the search tree is finitely branching. It is also desirable for showing consistency, since the biggest obstacle to showing consistency is the cut rule, which is ...

This condition is equivalent to the condition that k be existentially closed in the Laurent series field k((t)) [Pop96, Proposition 1.1]. It is in some sense opposite to the “Mordellic” properties satisfied by number fields, over which curves of genus greater than 1 have finitely many rational points [Fal83]. If p is any prime number, then any p-field (field for which all finite extensions are ...

Under the assumption that the Polynomial-Time Hierarchy does not collapse we show for a regular language L: The unbalanced polynomialtime leaf language class determined by L equals NP i L is existentially but not quanti erfree de nable in FO[<;min;max;+1; 1]. Furthermore, no such class lies properly between NP and co-1-NP or NP co-NP. The proofs rely on a result of Pin & Weil [9] characterizing...

Abstract In this paper we introduce the notion of existentially closed Leibniz algebras. Then use HNN-extensions algebras in order to prove an embedding theorem.

We study the model theory of vector spaces with a bilinear form over fixed field. For finite fields this can be, and has been, done in classical framework full first-order logic. infinite we need different logical frameworks. First take category-theoretic approach, which requires very little set-up. show that linear independence forms simple unstable relation. With some more work then also posi...