Related papers: Biba's trick, with applications

We present a new structure theorem for finite fields of odd order that relates multiplicative and additive structure in an interesting way. This theorem has several applications, including an improved understanding of Dickson and Chebyshev…

S. Kov\'acs proposed a conjecture on rigidity results induced by ample subsheaves of some exterior power of tangent bundles for projective manifolds. We verify the conjecture in the case of second exterior products under a rank condition.…

Forcing axioms are generalizations of Baire category principles that allow one to intersect more dense open sets and to do so in a wider variety of circumstances. In this paper we introduce two new forcing axioms related to posets which…

We show that many countable support iterations of proper forcings preserve Souslin trees. We establish sufficient conditions in terms of games and we draw connections to other preservation properties. We present a proof of preservation…

We describe new methods for deciding the stability of switching systems. The methods build on two ideas previously appeared in the literature: the polytope norm iterative construction, and the lifting procedure. Moreover, the combination of…

In studying the structure of derived categories of module categories of group algebras or their blocks, it is fundamental to classify support $\tau$-tilting modules. Koshio and Kozakai showed that the structure of support $\tau$-tilting…

In this paper, we prove some rigidity theorems for compact Bach-flat $n$-manifold with the positive constant scalar curvature. In particular, our conditions in Theorem 1.4 have the additional properties of being sharp.

We develop new techniques for constructing model structures from a given class of cofibrations, together with a class of fibrant objects and a choice of weak equivalences between them. As a special case, we obtain a more flexible version of…

We revisit classical gradient characterizations of quasiconvexity and provide corrected proofs that close gaps in earlier arguments. For the differentiable case of $\sigma$-quasiconvexity, we establish the full equivalence between several…

We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a $\Pi^1_2$…

We show that the equational theory of the structure $\langle \omega^{\omega}: (x,y)\mapsto x+y, x\mapsto \omega x \rangle $ is finitely axiomatizable and give a simple axiom schema when the domain is the set of transfinite ordinals. We give…

We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.

We describe a variation of Ash's $\eta$-system, and give a new proof of Ash's metatheorem. As an application, we prove a generalization of Ash and Knight's theorem on pairs of structures.

We define a nontrivial version of the square principle $\Box_\omega$, which we then show consistent by means of forcing with finite conditions. This paper has been withdrawn by the author due to the fact that the presented $\Box_\omega$ can…

We develop a forcing framework based on the idea of amalgamating language fragments into a theory with a canonical term model. We then demonstrate the usefulness of this framework by applying it to variants of the extended Namba problem, as…

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…

We note that some form of the condition "$p_1, p_2$ have a $\leq_{\mathbb{Q}}$-lub in $\mathbb{Q}$" is necessary in some forcing axiom for $\lambda$-complete $\mu^+$-c.c. forcing notions. We also show some versions are really stronger than…

In this article we generalize a theorem by Palais on the rigidity of compact group actions to cotangent lifts. We use this result to prove rigidity for integrable systems on symplectic manifolds including sytems with degenerate…

We give a simple proof for the rigidity of a complex in the bounded derived category of sheaves with constructible cohomology on an abelian variety.

This paper will develop a single framework for unifying, simplifying and extending our prior results about axiom systems that retain a partial knowledge of their own consistency, via an axiomatic declaration of self-consistency. Its perhaps…