Shifting the focus from fear, guilt, and indignation related to deteriorating environmental quality, the authors hypothesized that people who see greater potential for restorative experiences in natural environments also do more to protect them by behaving ecologically, as with recycling or reduced driving. University students rated a familiar freshwater marsh in terms of being away, fascination, coherence, and compatibility, qualities of restorative person-environment transactions described in attention restoration theory. They also reported on their performance of various ecological behaviors. The authors (...) tested a structural equation model with data from a randomly drawn subset of participants and then confirmed it with the data from a second subset. For the combined subsets, perceptions of the restorative qualities predicted 23% of the variance in general ecological behavior. As the only direct predictor, fascination mediated the influences of coherence, being away, and compatibility. (shrink)

Name der Zeitschrift: Studies in Logic, Grammar and Rhetoric Jahrgang: 45 Heft: 1 Seiten: 69-86.

The fast recovery of Germany's economy after World War II—the so‐called “German miracle”—can be explained by the market‐oriented economic policies pursued in the 1950s, based upon the ideas of Ordoliberalism. The slounng growth rates and increasing economic difficulties since the 1970s seem to have resulted from the extension of interventionist and redistributionist policies beyond those sanctioned by Ordoliberalism. The roots of the German economic decline are political: already in the 1950s, a broad consensus existed about the need to integrate market‐oriented (...) economic policy with a highly redistributory welfare state in a “social market economy.”. (shrink)

Restoration skills training is a mindfulness-based course in which participants draw support from a natural practice setting while they learn to meditate. Well-established conventional mindfulness training can improve psychological functioning but many perceive it as demanding and fail to sustain practice habits. Applying non-inferiority logic, previous research indicated that ReST overcomes compliance problems without compromising the benefits gained over 5 weeks’ training. This article applies similar logic in a 6-month follow-up. Of 97 contacted ReST and CMT course completers, 68 responded (...) and 29 were included with multiple imputation data. The online survey included questions about their psychological functioning in three domains and the forms and frequencies with which they had continued to practice mindfulness after the course. Former ReST participants continued, on average, to show higher dispositional mindfulness and fewer cognitive lapses compared to pre-course ratings. Improved psychological functioning in one or more domains was demonstrated by 35%, as determined by a reliable change index. Again, analyses detected no indications of any substantive disadvantages compared to the more demanding, established CMT approach. Compared to the CMT group, more ReST participants had also continued to practice at least occasionally. Continued practice was linked to sustained improvements for ReST but not clearly so for CMT. ReST participants thus continued to use the skills and sustained the improvements in psychological functioning that they had gained in the course, further supporting the utility of ReST as a health intervention. (shrink)

A fundamental notion in a large part of mathematics is the notion of equicardinality. The language with Hartig quantifier is, roughly speaking, a first-order language in which the notion of equicardinality is expressible. Thus this language, denoted by LI, is in some sense very natural and has in consequence special interest. Properties of LI are studied in many papers. In [BF, Chapter VI] there is a short survey of some known results about LI. We feel that a more extensive (...) exposition of these results is needed. The aim of this paper is to give an overview of the present knowledge about the language LI and list a selection of open problems concerning it. After the Introduction $(\S1)$ , in $\S\S2$ and 3 we give the fundamental results about LI. In $\S4$ the known model-theoretic properties are discussed. The next section is devoted to properties of mathematical theories in LI. In $\S6$ the spectra of sentences of LI are discussed, and $\S7$ is devoted to properties of LI which depend on set-theoretic assumptions. The paper finishes with a list of open problem and an extensive bibliography. The bibliography contains not only papers we refer to but also all papers known to us containing results about the language with Hartig quantifier. Contents. $\S1$ . Introduction. $\S2$ . Preliminaries. $\S3$ . Basic results. $\S4$ . Model-theoretic properties of $LI. \S5$ . Decidability of theories with $I. \S6$ . Spectra of LI- sentences. $\S7$ . Independence results. $\S8$ . What is not yet known about LI. Bibliography. (shrink)

We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded subclasses $P, Q, {\langle L[P],\in,P \rangle }$ and ${\langle L[Q],\in,Q \rangle }$ possess the same reals, satisfy the Generalised Continuum Hypothesis, and moreover are elementarily equivalent. Examples of such P are Card, the class of uncountable cardinals, I the uniform indiscernibles, or for any n the class $C^{n}{=_{{\operatorname {df}}}}\{ \lambda \, | \, (...) V_{\lambda } \prec _{{\Sigma }_{n}}V\}$ ; moreover the theory of such models is invariant under ZFC-preserving extensions. They also all have a rich structure satisfying many of the usual combinatorial principles and a definable wellorder of the reals. The inner model constructed using definability in the language augmented by the Härtig quantifier is thus also characterized. (shrink)

Restorativeness is defined as the potential of the environment to re-establish certain cognitive capacities related to human information processing. The most frequently used instrument for evaluating the restorativeness of places is the Perceived Restorativeness Scale, proposed by Hartig and colleagues (1991). Later on, shorter versions of the Perceived Restorativeness Scale were proposed. The aim of this work is to evaluate the discriminatory capacity of the original and of a shorter Spanish version of the PRS, considering urban settings previously selected (...) for having different level of restorativeness, according to expert’s criteria. The study involved 244 students and used a 3 x 2 mixed experimental design, with two independent variables: Restorativeness of a place (between-subjects), which was manipulated by showing pictures of settings selected with varying levels of restorativeness (high, medium, low), and length of the scale (within-subjects), which was manipulated by asking subjects to fill in both the original and a shorter version of the PRS. The order of presentation of the two scales was counterbalanced. Results show an appropriate reliability for both version of the scale. Items of being-away, fascination, and coherence of the shorter scale correlate more strongly with the corresponding factor of the original scale, compared to the others factors. Both scales produce similar values for the perceived restorativeness of the different places, except for places with low restorativeness. (shrink)

We show that the predicate “x is the power set of y” is ‐definable, if V = L[E] is an extender model constructed from a coherent sequences of extenders, provided that there is no inner model with a Woodin cardinal. Here is a predicate true of just the infinite cardinals. From this we conclude: the validities of second order logic are reducible to, the set of validities of the Härtig quantifier logic. Further we show that if no L[E] model has (...) a cardinal strong up to one of its ℵ‐fixed points, and, the Löwenheim number of this logic, is less than the least weakly inaccessible δ, then (i) is a limit of measurable cardinals of K, and (ii) the Weak Covering Lemma holds at δ. (shrink)

We show that, assuming the consistency of a supercompact cardinal, the first inaccessible cardinal can satisfy a strong form of a Löwenheim–Skolem–Tarski theorem for the equicardinality logic L, a logic introduced in [5] strictly between first order logic and second order logic. On the other hand we show that in the light of present day inner model technology, nothing short of a supercompact cardinal suffices for this result. In particular, we show that the Löwenheim–Skolem–Tarski theorem for the equicardinality logic at (...) κ implies the Singular Cardinals Hypothesis above κ as well as Projective Determinacy. (shrink)

First-order logic is known to have a severely limited expressive power on finite structures. As a result, several different extensions have been investigated, including fragments of second-order logic, fixpoint logic, and the infinitary logic L∞ωω in which every formula has only a finite number of variables. In this paper, we study generalized quantifiers in the realm of finite structures and combine them with the infinitary logic L∞ωω to obtain the logics L∞ωω, where Q = {Qi: iε I} is a family (...) of generalized quantifiers on finite structures. Using the logics L∞ωω, we can express polynomial-time properties that are not definable in L∞ωω, such as “there is an even number of x” and “there exists at least n/2 x” , without going to second-order logic. We show that equivalence of finite structures relative to L∞ωω can be characterized in terms of certain pebble games that are a variant of the Ehrenfeucht—Fraïssé games. We combine this game-theoretic characterization with sophisticated combinatorial tools from Ramsey theory, such as van der Waerden's Theorem and Folkman's Theorem, in order to investigate the scope and limits of generalized quantifiers in finite model theory. We obtain sharp lower bounds for expressibility in the logics L∞ωω and discover an intrinsic difference between adding finitely many simple unary generalized quantifiers to L∞ωω adding infinitely many. In particular, we show that if Qis a finite sequence of simple unary generalized quantifiers, then the equicardinality, or Härtig, quantifier is not definable in L∞ωω. We also show that the query “does the equivalence relation E have an even number of equivalence classes” is not definable in the extension L∞ωω of L∞ωω by the Härtig quantifier I and any finite sequence Q of simple unary generalized quantifiers. (shrink)

The following problem is studied: How large and how small can the Löwenheim and Hanf numbers of unbounded logics be in relation to the most common large cardinals? The main result is that the Löwenheim number of the logic with the Härtig-quantifier can be consistently put in between any two of the first weakly inaccessible, the first weakly Mahlo, the first weakly compact, the first Ramsey, the first measurable and the first supercompact cardinals.

A combinatorial criterium is given when a monadic quantifier is expressible by means of universe-independent monadic quantifiers of width n. It is proved that the corresponding hierarchy does not collapse. As an application, it is shown that the second resumption (or vectorization) of the Hartig quantifier is not definable by monadic quantifiers. The techniques rely on Ramsey theory.

It is a classical result of Mortimer that $L^2$ , first-order logic with two variables, is decidable for satisfiability. We show that going beyond $L^2$ by adding any one of the following leads to an undecidable logic:– very weak forms of recursion, viz.¶(i) transitive closure operations¶(ii) (restricted) monadic fixed-point operations¶– weak access to cardinalities, through the Härtig (or equicardinality) quantifier¶– a choice construct known as Hilbert's $\epsilon$ -operator.In fact all these extensions of $L^2$ prove to be undecidable both for satisfiability, (...) and for satisfiability in finite structures. Moreover most of them are hard for $\Sigma^1_1$ , the first level of the analytical hierachy, and thus have a much higher degree of undecidability than first-order logic. (shrink)

We prove some results about the limitations of the expressive power of quantifiers on finite structures. We define the concept of a bounded quantifier and prove that every relativizing quantifier which is bounded is already first-order definable (Theorem 3.8). We weaken the concept of congruence closed (see [6]) to weakly congruence closed by restricting to congruence relations where all classes have the same size. Adapting the concept of a thin quantifier (Caicedo [1]) to the framework of finite structures, we define (...) the concept of a meager quantifier. We show that no proper extension of first-order logic by means of meager quantifiers is weakly congruence closed (Theorem 4.9). We prove the failure of the full congruence closure property for logics which extend first-order logic by means of meager quantifiers, arbitrary monadic quantifiers, and the Härtig quantifier (Theorem 6.1). (shrink)

Einleitend wird über die vielfältigen Vorteile wissenschaftlichen Arbeitens im Alter geschrieben. Die fünf Aufsätze des Buches widmen sich Randbereichen philosophischen Denkens. Auf dem Lande war vom 16. bis zum 19. Jahrhundert von Akademikern nur der Pfarrer gefragt, statt der akademisch gebildeten Mediziner nutzte man die aus dem Handwerk (z.B. Bader) herkommenden "Volksmediziner". Ebenso Astrologie und Alchemie. Die Dorfschullehrer hatten ebenfalls keine akademische Ausbildung. Über Philipp Melanchthon gibt es eine Vielzahl von Literatur. Sein Verhältnis zu den verschiedenen Richtungen der Häretiker, so (...) zu den Täufern, den Unitariern, zu Sebastian Franck und Caspar von Schwenckfeld ist bislang aber weniger behandelt. Auch der Chiliasmus des 16. und 17. Jahrhunderts ist gleich Utopie, Apokalyptik, Messianismus oder Eschatologie in Deutschland relativ selten philosophisches Arbeitsgebiet. Das gilt auch für Ehrenfried Walther von Tschirnhaus, Christian Weise und Johann Jakob von Hartig, "drei Glanzlichter der Oberlausitz". Bei Moses Mendelssohn wird vornehmlich seine Toleranzposition von 1782 dargelegt, dabei Toleranz und Intoleranz auch in Staat und Kirche bestimmt"--Back cover. (shrink)