Let p be an odd prime. A method is described which given a structure M of finite similarity type produces a nilpotent group of class 2 and exponent p which is in the same stability class as M. Theorem. There are nilpotent groups of class 2 and exponent p in all stability classes. Theorem. The problem of characterizing a stability class is equivalent to characterizing the (nilpotent, class 2, exponent p) groups in that class.

We study descriptive set theory in the space ω1 ω 1 by letting trees with no uncountable branches play a similar role as countable ordinals in traditional descriptive set theory. By using such trees, we get, for example, a covering property for the class of Π 1 1 -sets of ω1 ω 1 . We call a family U of trees universal for a class V of trees if $\mathscr{U} \subseteq \mathscr{V}$ and every tree in V can be order-preservingly mapped (...) into a tree in U. It is well known that the class of countable trees with no infinite branches has a universal family of size ℵ 1 . We shall study the smallest cardinality of a universal family for the class of trees of cardinality ≤ℵ 1 with no uncountable branches. We prove that this cardinality can be 1 (under ¬CH) and any regular cardinal κ which satisfies ℵ 2 ≤ κ ≤ 2 ℵ 1 (under CH). This bears immediately on the covering property of the Π 1 1 -subsets of the space ω1 ω 1 . We also study the possible cardinalities of definable subsets of ω1 ω 1 . We show that the statement that every definable subset of ω1 ω 1 has cardinality $ or cardinality 2 ω1 is equiconsistent with ZFC (if n ≥ 3) and with ZFC plus an inaccessible (if n = 2). Finally, we define an analogue of the notion of a Borel set for the space ω1 ω 1 and prove a Souslin-Kleene type theorem for this notion. (shrink)

Most people encounter art images as digital reproductions on a computer screen instead of as originals in a museum or gallery. With the development of digital technologies, high-resolution artworks can be accessed anywhere and anytime by a large number of viewers. Since these digital images depict the same content and are attributed to the same artist as the original, it is often implicitly assumed that their aesthetic evaluation will be similar. When it comes to the digital reproductions of art, however, (...) it is also obvious that reproductions do differ from the originals in various aspects. Besides image quality, resolution, and format, the most obvious change is in the representation of color. The effects of subjectively varying surface-level image features on art evaluation have not been clearly assessed. To address this gap, we compare the evaluation of digital reproductions of 16 expressionist and impressionist paintings manipulated to have a high color saturation vs. a saturation similar to the original. We also investigate the impact of viewing time and expertise, two other aspects that may impact the perception of art in online contexts. Moreover, we link these dimensions to a recent model of aesthetic experience [the Vienna Integrated Model of Top-Down and Bottom-Up Processes in Art Perception ]. Results suggest that color saturation does not exert a major influence on liking. Cognitive and emotional aspects, however, are affected – to different extents for experts and laypersons. For laypersons, the increase in color saturation led to more positive assessments of an artwork, whereas it resulted in increased confusion for art experts. This insight is particularly important when it comes to reproducing artworks digitally. Depending on the intended use, increasing or decreasing the color saturation of the digitally reproduced image might be most appropriate. We conclude with a discussion of these findings and address the question of why empirical aesthetics requires more precise dimensions to better understand the subtle processes that take place in the perception of today’s digitally reproduced art environment. (shrink)

It is consistent with ¬CH that every universal theory of relational structures with the joint embedding property and amalgamation for P --diagrams has a universal model of cardinality ℵ 1. For classes with amalgamation for P --diagrams it is consistent that $2^{\aleph_0} > \aleph_2$ and there is a universal model of cardinality ℵ 2.

c.c.c. posets are characterised in terms of N-generic conditions. This characterisation can be applied to get simple proofs of many facts about c.c.c. forcing including $\operatorname{Con}(MA + \neg CH)$.

It is consistent that for many cardinals λ there is a family of at least λ + unbounded subsets of λ which have uniformization properties. In particular if it is consistent that a supercompact cardinal exists, then it is consistent that ℵ ω has such a family. We have applications to point set topology, Whitehead groups and reconstructing separable abelian p-groups from their socles.

We study descriptive set theory in the space $^{\omega_1}\omega_1$ by letting trees with no uncountable branches play a similar role as countable ordinals in traditional descriptive set theory. By using such trees, we get, for example, a covering property for the class of $\Pi^1_1$-sets of $^{\omega_1}\omega_1$. We call a family $\mathscr{U}$ of trees universal for a class $\mathscr{V}$ of trees if $\mathscr{U} \subseteq \mathscr{V}$ and every tree in $\mathscr{V}$ can be order-preservingly mapped into a tree in $\mathscr{U}$. It is well (...) known that the class of countable trees with no infinite branches has a universal family of size $\aleph_1$. We shall study the smallest cardinality of a universal family for the class of trees of cardinality $\leq\aleph_1$ with no uncountable branches. We prove that this cardinality can be 1 (under $\neg$CH) and any regular cardinal $\kappa$ which satisfies $\aleph_2 \leq \kappa \leq 2^{\aleph_1}$ (under CH). This bears immediately on the covering property of the $\Pi^1_1$-subsets of the space $^{\omega_1}\omega_1$. We also study the possible cardinalities of definable subsets of $^{\omega_1}\omega_1$. We show that the statement that every definable subset of $^{\omega_1}\omega_1$ has cardinality $<\omega_n$ or cardinality $2^{\omega_1}$ is equiconsistent with ZFC (if $n \geq 3$) and with ZFC plus an inaccessible (if $n = 2$). Finally, we define an analogue of the notion of a Borel set for the space $^{\omega_1}\omega_1$ and prove a Souslin-Kleene type theorem for this notion. (shrink)

Player motivation is a key research area within games research, with the aim of understanding how the motivation of players is related to their experience and behavior in the game. We present the results of a cross-sectional study with data from 750 players of League of Legends, a popular Multiplayer Online Battle Arena game. Based on the motivational regulations posited by Self-Determination Theory and Latent Profile Analysis, we identify four distinct motivational profiles, which differ with regards to player experience and, (...) to a lesser extent, in-game behavior. While the more self-determined profiles "Intrinsic" and "Autonomous" report mainly positive experience-related outcomes, a considerable part of the player base does not. Players of the "Amotivated" and "External" profile derive less enjoyment, experience more negative affect and tension, and score lower on vitality, indicating game engagement that is potentially detrimental to players' well-being. With regards to game metrics, minor differences in the rate of assists in unranked matches and performance indicators were observed between profiles. This strengthens the notion that differences in experiences are not necessarily reflected in differences in behavioral game metrics. Our findings provide insights into the interplay of player motivation, experience, and in-game behavior, contributing to a more nuanced understanding of player-computer interaction. (shrink)

A partially ordered set is called k-homogeneous if any isomorphism between k-element subsets extends to an automorphism of . Assuming the set-theoretic assumption ⋄, it is shown that for each k, there exist partially ordered sets of size ϰ1 which embed each countable partial order and are k-homogeneous, but not -homogeneous. This is impossible in the countable case for k ≥ 4.

It is consistent with $\neg\mathrm{CH}$ that every universal theory of relational structures with the joint embedding property and amalgamation for $\mathscr{P}^-(3)$-diagrams has a universal model of cardinality $\aleph_1$. For classes with amalgamation for $\mathscr{P}^-(4)$-diagrams it is consistent that $2^{\aleph_0} > \aleph_2$ and there is a universal model of cardinality $\aleph_2$.