逻辑
The satisfiability problem for multilevel syllogistic extended with the Cartesian product operator (MLSC) is a long-standing open problem in computable set theory. For long, it was not excluded that such a problem were undecidable, due to…
Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I…
We propose a categorical and algebraic study of quantale modules. The results and constructions presented are also applied to abstract algebraic logic and to image processing tasks.
Under no additional assumptions, in this paper we construct a Ramsey expansion for every category of finite objects with finite small Ramsey degrees. Our construction is based on the relationship between small Ramsey degrees, weak…
This paper is concerned with the model-theoretic study of pairs $(K,F)$ where $K$ is an algebraically closed field and $F$ is a distinguished subfield of $K$ allowing extra structure. We study the basic model-theoretic properties of those…
We remark that forcing on fiber bundles of structures of first order languages is not a compatible semantics with the pullback (of fiber bundles) and we describe a semantics which behaves well with respect to it. This new semantics uses…
We provide a general preservation theorem for preserving selective independent families along countable support iterations. The theorem gives a general framework for a number of results in the literature concerning models in which the…
Hardin and Taylor \cite{MR2384262} proved that any function on the reals -- even a nowhere continuous one -- can be correctly predicted, based solely on its past behavior, at almost every point in time. They showed in \cite{MR3100500} that…
We show that there is no theory that is minimal with respect to interpretability among recursively enumerable essentially undecidable theories.
Recall that a group $G$ has finitely satisfiable generics ($fsg$) or definable $f$-generics ($dfg$) if there is a global type $p$ on $G$ and a small model $M_0$ such that every left translate of $p$ is finitely satisfiable in $M_0$ or…
We consider interpretable topological spaces and topological groups in a $p$-adically closed field $K$. We identify a special class of "admissible topologies" with topological tameness properties like generic continuity, similar to the…
We describe a syntactic method for taking proofs which use ultraproducts and translating them into direct, constructive proofs.
There are Noetherian rings (in fact domains) with a free additive group, in every infinite cardinality. (This is an expanded version of [SgSh:217] which appears in the Abstracts of the American Mathematical Society 7 (1986): 369.)
In this paper we prove a Robinson consistency theorem for a class of many-sorted hybrid logics as a consequence of an Omitting Types Theorem. An important corollary of this result is an interpolation theorem.
In this article we define restricted log-exp-analytic functions as compositions of log-analytic functions and exponentials whose logarithm are locally bounded. We prove that the derivative of a restricted log-exp-analytic function is again…
We give a normal five-valued truth-table proving independence of one of the axioms in Robinson's set of axioms for propositional calculus from 1968, answering a question raised in his article, where he uses a non-normal truth-table. We also…
There exist NIP and non-NTP$_2$ theories satisfying all the following conditions: It is not o-minimal; All models are strongly locally o-minimal; It has a model which is an expansion of the linearly ordered abelian group over the reals…
Within Bishop Set Theory, a reconstruction of Bishop's theory of sets, we study the so-called completely separated sets, that is sets equipped with a positive notion of an inequality, induced by a given set of real-valued functions. We…
We begin the investigation of the variety of semilattices of Mal'cev blocks, which we call SMB algebras.
In this paper, we introduce a logic based on team semantics, called FOT, whose expressive power is elementary, i.e., coincides with first-order logic both on the level of sentences and (possibly open) formulas, and we also show that a…