# Mathematical Logic Quarterly

Mathematical Logic Quarterly > 56 > 1 > 78 - 84

Mathematical Logic Quarterly > 56 > 1 > 85 - 88

Mathematical Logic Quarterly > 56 > 1 > 89 - 102

Mathematical Logic Quarterly > 56 > 1 > 29 - 34

**IP**) does not imply its outer form (

**OP**). We also show that

**OP**can be properly split into

**IP**and the weak Pasch axiom (

**WP**) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mathematical Logic Quarterly > 56 > 1 > 51 - 62

*MV*‐algebra and we obtain some related results. After that by considering the notions ofhyper

*MV*‐ideals and weak hyper

*MV*‐ideals, we prove some theorems. Then we determine relationships between (weak) hyper

*MV*‐ideals in a hyper

*MV*‐algebra (

*M*, ⊕, *, 0) and (weak) hyper

*K*‐ideals in a hyper

*K*‐algebra (

*M*, °, 0). Finally we give a...

Mathematical Logic Quarterly > 56 > 1 > 35 - 41

*SU*‐rank 1 structures and the properties of “generic” pairs of such structures, started in [8]. In particular, we show that the SU‐rank of the (complete) theory of generic pairs of models of an

*SU*‐rank 1 theory

*T*can only take values 1 (if and only if

*T*is trivial), 2 (if and only if

*T*is linear) or

*ω*, generalizing the...

Mathematical Logic Quarterly > 56 > 1 > 4 - 12

Mathematical Logic Quarterly > 56 > 1 > 63 - 66

Mathematical Logic Quarterly > 56 > 1 > 42 - 50

Mathematical Logic Quarterly > 56 > 1 > 103 - 112

*α*the class of polyadic algebras of dimension

*α*has the super amalgamation property (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Mathematical Logic Quarterly > 56 > 1 > 67 - 77

Mathematical Logic Quarterly > 56 > 1 > 13 - 28

Mathematical Logic Quarterly > 56 > 2 > 159 - 163

_{0}‐categorical coloured linear orders, generalizing Rosenstein's characterization of ℵ

_{0}‐categorical linear orderings. We show that they can all be built from coloured singletons by concatenation and ℚ

_{n}‐combinations (for

*n*≥ 1). We give a method using coding trees to describe all structures in our list (© 2010 WILEY‐VCH Verlag GmbH &...

Mathematical Logic Quarterly > 56 > 2 > 148 - 158

Mathematical Logic Quarterly > 56 > 2 > 164 - 170

_{1}to be regular and for ℵ${\text{\hspace{0.17em}}}_{\text{\omega}{\text{\hspace{0.17em}}}_{\text{1}}\text{+1}}$ to be measurable and to carry precisely

*τ*normal measures, where

*τ*≥ ℵ${\text{\hspace{0.17em}}}_{{\text{\hspace{0.17em}}}_{\text{\omega}}{\text{\hspace{0.17em}}}_{\text{1}}\text{+2}}$ is any regular cardinal. This extends the work of [2], in which the analogous result was obtained for ℵ

_{ω +1}using the same hypotheses (© 2010 WILEY‐VCH Verlag GmbH &...

Mathematical Logic Quarterly > 56 > 2 > 185 - 190

*n*elements (called

*n*‐ary partitions), for some integer

*n*. We show that if

*n*is odd, then a Russell‐set

*X*has an

*n*‐ary partition if and only if |

*X*| is divisible by

*n*. Furthermore, we establish that it is relative consistent with ZF that there exists...

Mathematical Logic Quarterly > 56 > 2 > 175 - 184

**be an additive subgroup of ℂ, let**

*G**W*

_{n}= {

*x*= 1,

_{i}*x*+

_{i}*x*=

_{j}*x*:

_{k}*i, j, k*∈ {1, …,

*n*}}, and define

*E*= {

_{n}*x*= 1,

_{i}*x*+

_{i}*x*=

_{j}*x*,

_{k}*x*·

_{i}*x*=

_{j}*x*:

_{k}*i, j, k*∈ {1, …,

*n*}}. We discuss two conjectures. (1) If a system

*S*⊆

*E*is consistent over ℝ (ℂ), then

_{n}*S*has a real (complex) solution which consists of numbers whose absolute values belong to [0, 2

^{2n –2}]. (2) If a system

*S*⊆

*W*is consistent over

_{n}**, then...**

*G*Mathematical Logic Quarterly > 56 > 2 > 216 - 224

*κ*‐covering set in connection with Bernstein sets and other types of non‐measurability. Our results correspond to those obtained by Muthuvel in [7] and Nowik in [8]. We consider also other types of coverings (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)