相关论文: Omega-powers and descriptive set theory

In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…

This thesis presents an alternative to Cantor's theory of cardinality, insofar as that is understood as a theory of set size. The alternative is based on a general theory, ClassSize. ClassSize contains all sentences in the first order…

We propose FC, a new logic on words that combines finite model theory with the theory of concatenation - a first-order logic that is based on word equations. Like the theory of concatenation, FC is built around word equations; in contrast…

We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined…

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…

We study first-order model checking, by which we refer to the problem of deciding whether or not a given first-order sentence is satisfied by a given finite structure. In particular, we aim to understand on which sets of sentences this…

We consider strong expansions of the theory of ordered abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of definable sets in such theories, in particular as relates to…

Category theory provides a powerful tool to organize mathematics. A sample of this descriptive power is given by the categorical analysis of the practice of "classes as shorthands" in ZF set theory. In this case category theory provides a…

This paper is the extended version of On the Complexity of Infinite Advice Strings (ICALP 2018). We investigate a notion of comparison between infinite strings. In a general way, if M is a computation model (e.g. Turing machines) and C a…

We generalize the notion of saturated order to infinite partial orders and give both a set-theoretic and an algebraic characterization of such orders. We then study the proof theoretic strength of the equivalence of these characterizations…

We study the links between the topological complexity of an omega context free language and its degree of ambiguity. In particular, using known facts from classical descriptive set theory, we prove that non Borel omega context free…

Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…

We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…

Given a totally finite ordered alphabet $ A $, endowing the set of words over $ A $ with the alternating lexicographic order, we define a new class of Lyndon words. We study the fundamental properties of the associated symbolic dynamical…

Metaphysical interpretations of set theory are either inconsistent or incoherent. The uses of sets in mathematics actually involve three distinct kinds of collections (surveyable, definite, and heuristic), which are governed by three…

Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper we study the generalization where countable is replaced by uncountable. We explore properties of generalized…

We consider the logic MSO+U, which is monadic second-order logic extended with the unbounding quantifier. The unbounding quantifier is used to say that a property of finite sets holds for sets of arbitrarily large size. We prove that the…

In this paper we explore a connection between descriptive set theory and inner model theory. From descriptive set theory, we will take a countable, definable set of reals, A. We will then show that A is equal to the reals of M, where M is a…

A complete partition theory is presented for omega-located words (and omega-words), namely for located words over an infinite alphabet dominated by a fixed increasing sequence. This theory strengthens in an essential way the classical…

We characterize the squares occurring in infinite overlap-free binary words and construct various alpha power-free binary words containing infinitely many overlaps.