Spatiality and classical logic

In this short note we show that any proof of a general spatiality theorem for inductively generated formal topologies requires full classical logic. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Biprobability logic with conditional expectation

This paper is devoted to fill the gap in studying logics for biprobability structures. We introduce the logic $L_{\mathbb AE_1E_2}^a$ with two conditional expectation operators and prove the completeness theorem. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Nisan‐Wigderson generators in proof systems with forms of interpolation

We prove that the Nisan‐Wigderson generators based on computationally hard functions and suitable matrices are hard for propositional proof systems that admit feasible interpolation. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Quantifier‐eliminable locally finite graphs

We identify the locally finite graphs that are quantifier‐eliminable and their first order theories in the signature of distance predicates. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Powers of positive elements in C*‐algebras

In this paper, we show that Ogasawa’s theorem has a proof in Bishop style constructive mathematics (BISH). In 25 , we introduced the elementary constructive theory of C*‐algebras in BISH, but we did not discuss the powers of positive elements there. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

On definability of types of finite Cantor‐Bendixson rank

We prove that every type of finite Cantor‐Bendixson rank over a model of a first‐order theory without the strict order property is definable and has a unique nonforking extension to a global type. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

On quasi‐varieties of multiple valued logic models

We extend the concept of quasi‐variety of first‐order models from classical logic to multiple valued logic (MVL) and study the relationship between quasi‐varieties and existence of initial models in MVL. We define a concept of ‘Horn sentence’ in MVL and based upon our study of quasi‐varieties of MVL models we derive the existence of initial models for MVL ‘Horn theories’. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

On the absolutely continuous spectrum of block operator matrices

We prove an abstract theorem on the preservation of the absolutely continuous spectrum for block operator matrices. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The finiteness of compact Boolean algebras

We show that it consistent with Zermelo‐Fraenkel set theory that there is an infinite, compact Boolean algebra (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On monotone hull operations

We extend results of Elekes and Máthé on monotone Borel hulls to an abstract setting of measurable space with negligibles. This scheme yields the respective theorems in the case of category and in the cases associated with the Mendez σ‐ideals on the plane. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

On proximal convergence in uniform spaces

The paper deals with proximal convergence and Leader's theorem, in the constructive theory of uniform apartness spaces. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simple monadic theories and partition width

We study tree‐like decompositions of models of a theory and a related complexity measure called partition width. We prove a dichotomy concerning partition width and definable pairing functions: either the partition width of models is bounded, or the theory admits definable pairing functions. Our proof rests on structure results concerning indiscernible sequences and finitely satisfiable types for theories without definable pairing functions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Function theory in real Hardy spaces

We show that many classical results in Hardy space theory have exact analogues when the Fourier coefficients are restricted to be real. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Weak saturation of ideals on Pκ(λ)

We show that if κ is an infinite successor cardinal, and λ > κ a cardinal of cofinality less than κ satisfying certain conditions, then no (proper, fine, κ‐complete) ideal on P_κ(λ) is weakly λ⁺‐saturated. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Almost sure central limit theorems for random fields

A general almost sure limit theorem is presented for random fields. It is applied to obtain almost sure versions of some (functional) central limit theorems. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Stokes problem in a periodic layer

We construct and justify the asymptotic representation at infinity of solutions to the Stokes problem in a three‐dimensional domain with periodic geometric structure, which is bounded in one dimension, e.g., a periodically perforated layer. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Comparison of Picard groups in dimension 1

We compare two Picard groups in dimension 1. Our proofs are constructive and the results generalize a theorem of J. Sands [11]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Ordinal arithmetic with simultaneously defined theta‐functions

This article provides a detailed comparison between two systems of collapsing functions. These functions play a crucial role in proof theory, in the analysis of patterns of resemblance, and the analysis of maximal order types of well partial orders. The exact correspondence given here serves as a starting point for far reaching extensions of current results on patterns and well partial orders. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

A spectral integral representation for decomposable operators

For the operators commuting with a spectral measure, a Bartle type integral representation in the spirit of the one provided by the spectral theorem for normal operators is obtained. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Strict Mittag‐Leffler modules

We characterize strict Mittag‐Leffler modules in terms of free realizations of positive primitive formulas, and rings over which (pure‐) projectives are trivial in terms of various notions of separability of (flat) strict Mittag‐Leffler modules. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim