Related papers: The Baire closure and its logic

The noise-type completion C of a noise-type Boolean algebra B is generally not the same as the closure of B. As shown in Part I (Introduction, Theorem 2), C consists of all complemented elements of the closure. It appears that C is the…

Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has only unary operations and whose clone of term operations is…

We say that binary relation E on a space X is a clopen graph on X iff E is symmetric and irreflexive and clopen relative to X x X minus its diagonal. Equivalently for distinct x, y in X there are open sets U,V with (x,y) in U x V and either…

A sequence of functions f_n: X -> R from a Baire space X to the reals is said to converge in category iff every subsequence has a subsequence which converges on all but a meager set. We show that if there exists a Souslin Tree then there…

We show that for any class of Boolean algebras with an associative operator, if it contains the complex algebra of (P(N), U), its equational theory is undecidable. Equivalently, any associative normal modal logic valid over the frame (P(N),…

Let $X$ be a closed subvariety of an abelian variety $A$ over a global function field $k$ such that the base change of $A$ to an algebraic closure does not have any positive dimensional isotrivial quotient. We prove that every adelic point…

Let $R$ be a reduced affine $\mathbb C$-algebra, with corresponding affine algebraic set $X$. Let $\mathcal C(X)$ be the ring of continuous (Euclidean topology) $\mathbb C$-valued functions on $X$. Brenner defined the \emph{continuous…

It is proved that if any Z-graded weak module for vertex operator algebra V is completely reducible, then V is rational and C_2-cofinite. That is, V is regular. This gives a natural characterization of regular vertex operator algebras.

To the symmetric space of the (positive half) of a real loop group, we attach a Borel--Serre type bordification and equip it with a Hausdorff topology. The attached boundary, indexed by certain rational parabolics of the loop group, is…

Toric varieties are a special class of rational varieties defined by equations of the form {\it monomial = monomial}. For a good brief survey of the history and role of toric varieties see [10]. Any toric variety $X$ contains a cover by…

We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but…

We show that for each of the following Banach spaces~$X$, the quotient algebra $\mathscr{B}(X)/\mathscr{I}$ has a unique algebra norm for every closed ideal $\mathscr{I}$ of $\mathscr{B}(X)\colon$ - $X=…

In this paper, we study module theoretic definitions of the Baer and related ring concepts. We say a module is s.Baer if the right annihilator of a nonempty subset of the module is generated by an idempotent in the ring. We show that s.Baer…

Let $X$ be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$-equivariant homology $\overline{H}_{\ast}^{S^1}(\mathcal{L}X,\mathbb{Q}) $ of the free loop…

As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…

Let $X$ denote an equivariant embedding of a connected reductive group $G$ over an algebraically closed field $k$. Let $B$ denote a Borel subgroup of $G$ and let $Z$ denote a $B \times B$-orbit closure in $X$. When the characteristic of $k$…

Looking at the finite \'etale congruence covers $X(p)$ of a complex algebraic variety $X$ equipped with a variation of integral polarized Hodge structures whose period map is quasi-finite, we show that both the minimal gonality among all…

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 say that a set $S$ is $\Delta^0_{(n)}(X)$ if membership of $n$ in $S$ is a $\Delta^0_{n}(X)$ question, uniformly in $n$. A set $X$ is low for $\Delta$-Feiner if every set $S$ that is $\Delta^0_{(n)}(X)$ is also…

Wieler has shown that every irreducible Smale space with totally disconnected stable sets is a solenoid (i.e., obtained via a stationary inverse limit construction). Using her construction, we show that the associated stable C*-algebra is…