Notes on Craig interpolation for LJ with strong negation

The Craig interpolation theorem is shown for an extended LJ with strong negation. A new simple proof of this theorem is obtained. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim © 2011 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     

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     

Groupwise density cannot be much bigger than the unbounded number

We prove that g (the groupwise density number) is smaller or equal to ??⁺, the successor of the minimal cardinality of an unbounded subset of ^ωω. This is true even for the version of ?? for groupwise dense ideals. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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     

A “Sup + C Inf” inequality for Liouville‐type equations with singular potentials

We generalize a Harnack‐type inequality (I. Shafrir, C. R. Acad. Sci. Paris, 315 (1992), 159–164), for solutions of Liouville equations to the case where the weight function may admit zeroes or singularities of power‐type |x|^2α, with α ∈ (?1, 1). © 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     

Boolos‐style proofs of limitative theorems

Boolos's proof of incompleteness is extended straightforwardly to yield simple “diagonalization‐free” proofs of some classical limitative theorems of logic. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gorenstein categories and Tate cohomology on projective schemes

We study Gorenstein categories. We show that such a category has Tate cohomological functors and Avramov–Martsinkovsky exact sequences connecting the Gorenstein relative, the absolute and the Tate cohomological functors. We show that such a category has what Hovey calls an injective model structure and also a projective model structure in case the category has enough projectives. As examples we show that if X is a locally Gorenstein projective scheme then the category ??????(X) of quasi‐coherent sheaves on X is such a category and so has these features. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on meromorphic convexity

We give examples of Stein domains D in C ² such that C ² ? D is either completely pluripolar or union of germs of (principal) hypersurfaces not intersecting D such that D fails to be meromorphically convex in C ². © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

On the Euler characteristic of definable groups

We show that in an arbitrary o‐minimal structure the following are equivalent: (i) conjugates of a definable subgroup of a definably connected, definably compact definable group cover the group if the o‐minimal Euler characteristic of the quotient is non zero; (ii) every infinite, definably connected, definably compact definable group has a non trivial torsion point (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the nuclearity of certain Cuntz‐Pimsner algebras

In the present paper, we give a short proof of the nuclearity property of a class of Cuntz‐Pimsner algebras associated with a Hilbert ??‐bimodule ??, where ?? is a separable and nuclear C *‐algebra. We assume that the left ??‐action on the bimodule ?? is given in terms of compact module operators and that ?? is direct summand of the standard Hilbert module over ?? (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lp (ℝn ) boundedness for higher commutators of singular integrals with rough kernels belonging to certain block spaces

In this paper, we prove the L^p (?ⁿ ) boundedness for higher commutators of singular integrals with rough kernels belonging to certain block spaces provided that 1 < p < ∞ (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Second homology of Lie superalgebras

The second homology of Lie superalgebras over a field of characteristic 0 extended over a supercommutative superalgebra A and their twisted version are obtained. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Corrigendum to “Weak Arithmetics and Kripke Models”

We give a corrected proof of the main result in the paper [2] mentioned in the title. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on the undecidability of the reachability problem for o‐minimal dynamical systems

In this paper we prove that the reachability problem is BSS‐undecidable for o‐minimal dynamical systems. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Binary types in ℵ0‐categorical weakly o‐minimal theories

Orthogonality of all families of pairwise weakly orthogonal 1‐types for ?₀‐categorical weakly o‐minimal theories of finite convexity rank has been proved in 6 . Here we prove orthogonality of all such families for binary 1‐types in an arbitrary ?₀‐categorical weakly o‐minimal theory and give an extended criterion for binarity of ?₀‐categorical weakly o‐minimal theories (additionally in terms of binarity of 1‐types). © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Construction of biorthogonal wavelet bases beginning from two multiresolutions

Starting from two given multiresolutions of L²(ℝ) we construct biorthogonal dyadic wavelet bases which are associated with these multiresolutions. (© 2004 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)