相关论文: The Borel monadic theory of order is decidable
We characterize the category of monads on $Set$ and the category of Lawvere theories that are equivalent to the category of regular equational theories.
We prove that any finite set $F\subset {\mathbb{Z}^2}$ that tiles ${\mathbb{Z}^2}$ by translations also admits a periodic tiling. As a consequence, the problem whether a given finite set $F$ tiles ${\mathbb{Z}^2}$ is decidable.
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…
The theory of addition in the domains of natural (N), integer (Z), rational (Q), real (R) and complex (C) numbers is decidable, so is the theory of multiplication in all those domains. By Godel's Incompleteness Theorem the theory of…
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…
We propose a natural theory SO axiomatizing the class of sets of ordinals in a model of ZFC set theory. Both theories possess equal logical strength. Constructibility theory in SO corresponds to a natural recursion theory on ordinals.
Abelian groups having partial orderings compatible with their binary operations have long been studied in the literature. In particular, lattice-ordered abelian groups constitute a universal-algebraic variety, and thus form a category which…
We show that the regularity of monomial ideals whose associated prime ideals are totally ordered by inclusion is linearly bounded.
Let $H$ and $K$ be the bosonizations of the Jordan and super Jordan plane by the group algebra of a cyclic group; the algebra $K$ projects onto an algebra $L$ that can be thought of as the quantum Borel of $\mathfrak{sl}(2)$ at $-1$. The…
We study algorithmic learning of algebraic structures. In our framework, a learner receives larger and larger pieces of an arbitrary copy of a computable structure and, at each stage, is required to output a conjecture about the isomorphism…
It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this…
We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula phi(X,x) that is positive in X, it is decidable whether the…
We consider the classification problem for several classes of countable structures which are "vertex-transitive", meaning that the automorphism group acts transitively on the elements. (This is sometimes called homogeneous.) We show that…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
The main theorem of this article is that every countable model of set theory M, including every well-founded model, is isomorphic to a submodel of its own constructible universe. In other words, there is an embedding $j:M\to L^M$ that is…
The structures $\langle M,\subseteq^M\rangle$ arising as the inclusion relation of a countable model of sufficient set theory $\langle M,\in^M\rangle$, whether well-founded or not, are all isomorphic. These structures $\langle…
In this paper, we introduce and investigate monadic NM-algebras: a variety of NM-algebras equipped with universal quantifiers. Also, we obtain some conditions under which monadic NM-algebras become monadic Boolean algebras. Besides, we show…
We show that the category of countable Borel equivalence relations (CBERs) is dually equivalent to the category of countable $\mathcal{L}_{\omega_1\omega}$ theories which admit a one-sorted interpretation of a particular theory we call…
Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. Each such set is described by a single Set Theory formula with parameters unrelated to other formulas. Exotic expressions involving…
Given a countable o-minimal theory T, we characterize the Borel complexity of isomorphism for countable models of T up to two model-theoretic invariants. If T admits a nonsimple type, then it is shown to be Borel complete by embedding the…