It was proved recently that Telgársky’s conjecture, which concerns partial information strategies in the Banach–Mazur game, fails in models of \. The proof introduces a combinatorial principle that is shown to follow from \, namely: \::Every separative poset \ with the \-cc contains a dense sub-poset \ such that \ for every \. We prove this principle is independent of \ and \, in the sense that \ does not imply \, and \ does not imply \ assuming the (...) consistency of a huge cardinal. We also consider the more specific question of whether \ holds with \ equal to the weight-\ measure algebra. We prove, again assuming the consistency of a huge cardinal, that the answer to this question is independent of \. (shrink)

Let S be the set of those α ∈ ω₂ that have cofinality ω₁. It is consistent relative to a measurable that the nonempty player wins the pressing down game of length ω₁, but not the Banach-Mazur game of length ω + 1 (both games starting with S).

The title question of the paper has its empirical origin in the form of an individual’s existential experience arising from the personal use of a computer, which we attempt to describe in the first section. The rest of the entire paper can be understood as a philosophical essay answering the question posed. First the connection between the main problem of the article and its “premonition” by mankind, which was expressed in the form of ancient myths and legends, is briefly suggested. (...) After shortly discussing the problems that early considerations of AI focused on, i.e. whether machines can think at all, we move on to reformulate our title question, about the possibility of outsmarting AI. This outsmarting will be understood by us in a rather limited way as to prevent a machine from completing its implemented task. To achieve this objective, after softly clarifying the basic terms, an analogy is built between the “outsmarting” of a machine by a human (the target domain) and the playing of a mathematical game between two players (the base domain), where this outsmarting is assigned a “winning strategy” in the certain game. This mathematical model is formed by games similar to Banach-Mazur games. The strict theorems of such games are then proved and applied to the target of the analogy. We then draw conclusions and look for counter-examples to our findings. The answer to the title question posed is negative, and it is not clear how far it should be taken seriously. (shrink)

When two people engage in a conversation, knowingly or unknowingly, they are playing a game. Players of such games have diverse objectives, or winning conditions: an applicant trying to convince her potential employer of her eligibility over that of a competitor, a prosecutor trying to convict a defendant, a politician trying to convince an electorate in a political debate, and so on. We argue that infinitary games offer a natural model for many structural characteristics of such conversations. We call (...) such games message exchange games, and we compare them to existing game theoretic frameworks used in linguistics—for example, signaling games—and show that message exchange games are needed to handle non-cooperative conversation. In this paper, we concentrate on conversational games where players’ interests are opposed. We provide a taxonomy of conversations based on their winning conditions, and we investigate some essential features of winning conditions like consistency and what we call rhetorical cooperativity. We show that these features make our games decomposition sensitive, a property we define formally in the paper. We show that this property has far-reaching implications for the existence of winning strategies and their complexity. There is a class of winning conditions for which message exchange games are equivalent to Banach- Mazur games, which have been extensively studied and enjoy nice topological results. But decomposition sensitive goals are much more the norm and much more interesting linguistically and philosophically. (shrink)

The general aim of this paper is to introduce some ideas of the theory of infinite topological games into the philosophical debate on supertasks. First, we discuss the elementary aspects of some infinite topological games, among them the Banach-Mazur game.Then it is shown that the Banach-Mazur game may be conceived as a Newtonian supertask.In section 4 we propose to conceive physical experiments as infinite games. This leads to the distinction between determined and undetermined experiments and the problem of (...) how it is related to that between determinism and indeter-minism. Finally the role of the Axiom of Choice as a source of indetermi-nacy of supertasks is discussed. (shrink)

It is well known that if the nonempty player of the Banach–Mazur game has a winning strategy on a space, then that space is Baire in all powers even in the box product topology. The converse of this implication may also be true: We know of no consistency result to the contrary. In this paper we establish the consistency of the converse relative to the consistency of the existence of a proper class of measurable cardinals.

We investigate the pressing down game and its relation to the Banach Mazur game. In particular we show: consistently, there is a nowhere precipitous normal ideal I on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\aleph_2}$$\end{document} such that player nonempty wins the pressing down game of length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\aleph_1}$$\end{document} on I even if player empty starts.

This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of Lp-computable functions with a size notion, by introducing Lp-computable Baire categories. We show that Lp-computable Baire categories satisfy the following three basic properties. Singleton sets {f } are meager, suitable infinite unions of meager sets are meager, and the whole space of Lp-computable functions is not meager. We give an alternative characterization of meager sets via Banach-Mazur games. We (...) study the convergence of Fourier series for Lp-computable functions and show that whereas for every p > 1, the Fourier series of every Lp-computable function f converges to f in the Lp norm, the set of L1-computable functions whose Fourier series does not diverge almost everywhere is meager. (shrink)

We consider two classical computability notions for functions mapping all computable real numbers to computable real numbers. It is clear that any function that is computable in the sense of Markov, i.e., computable with respect to a standard Gödel numbering of the computable real numbers, is computable in the sense of Banach and Mazur, i.e., it maps any computable sequence of real numbers to a computable sequence of real numbers. We show that the converse is not true. This solves a (...) long-standing open problem posed by Kushner. (shrink)

We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space without isolated points, X, in such a way that every sequentially continuous function from Cantor space to ℤ extends to a sequentially continuous function from X to ℝ. The second asserts an analogous property for Baire space relative to any inhabited locally non-compact CSM. Both results rely on having careful (...) constructive formulations of the concepts involved.As a first application, we derive new relationships between “continuity principles” asserting that all functions between specified metric spaces are pointwise continuous. In particular, we give conditions that imply the failure of the continuity principle “all functions from X to ℝ are continuous”, when X is an inhabited CSM without isolated points, and when X is an inhabited locally non-compact CSM. One situation in which the latter case applies is in models based on “domain realizability”, in which the failure of the continuity principle for any inhabited locally non-compact CSM, X, generalizes a result previously obtained by Escardó and Streicher in the special case X = C[0, 1].As a second application, we show that, when the notion of inhabited complete separable metric space without isolated points is interpreted in a recursion-theoretic setting, then, for any such space X, there exists a Banach-Mazur computable function from X to the computable real numbers that is not Markov computable. This generalizes a result obtained by Hertling in the special case that X is the space of computable real numbers. (shrink)

We prove two embedding and extension theorems in the context of the constructive theory of metric spaces. The first states that Cantor space embeds in any inhabited complete separable metric space (CSM) without isolated points, X, in such a way that every sequentially continuous function from Cantor space to ℤ extends to a sequentially continuous function from X to ℝ. The second asserts an analogous property for Baire space relative to any inhabited locally non‐compact CSM. Both results rely on having (...) careful constructive formulations of the concepts involved.As a first application, we derive new relationships between “continuity principles” asserting that all functions between specified metric spaces are pointwise continuous. In particular, we give conditions that imply the failure of the continuity principle “all functions from X to ℝ are continuous”, when X is an inhabited CSM without isolated points, and when X is an inhabited locally non‐compact CSM. One situation in which the latter case applies is in models based on “domain realizability”, in which the failure of the continuity principle for any inhabited locally non‐compact CSM, X, generalizes a result previously obtained by Escardó and Streicher in the special case X = C[0, 1].As a second application, we show that, when the notion of inhabited complete separable metric space without isolated points is interpreted in a recursion‐theoretic setting, then, for any such space X, there exists a Banach‐Mazur computable function from X to the computable real numbers that is not Markov computable. This generalizes a result obtained by Hertling in the special case that X is the space of computable real numbers. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

R. M. Friedberg demonstrated the existence of a recursive functional that agrees with no Banach-Mazur functional on the class of recursive functions. In this paper Friedberg's result is generalized to both α-recursive functionals and weak α-recursive functionals for all admissible ordinals α such that $\lambda , where α * is the Σ 1 -projectum of α and λ is the Σ 2 -cofinality of α. The theorem is also established for the metarecursive case, α = ω 1 , where α (...) * = λ = ω. (shrink)

We show that large fragments of MM, e. g. the tree property and stationary reflection, are preserved by strongly -game-closed forcings. PFA can be destroyed by a strongly -game-closed forcing but not by an ω2-closed.

In this paper we show that the Proper Forcing Axiom is preserved under forcing over any poset PP with the following property: In the generalized Banach–Mazur game over PP of length , Player II has a winning strategy which depends only on the current position and the ordinal indicating the number of moves made so far. By the current position we mean: The move just made by Player I for a successor stage, or the infimum of all the moves (...) made so far for a limit stage. As a consequence of this theorem, we introduce a weak form of the square principle and show that it is consistent with PFA. (shrink)

Schervish (1985b) showed that every forecasting system is noncalibrated for uncountably many data sequences that it might see. This result is strengthened here: from a topological point of view, failure of calibration is typical and calibration rare. Meanwhile, Bayesian forecasters are certain that they are calibrated---this invites worries about the connection between Bayesianism and rationality.

A notion of resource-bounded Baire category is developed for the class PC[0,1] of all polynomial-time computable real-valued functions on the unit interval. The meager subsets of PC[0,1] are characterized in terms of resource-bounded Banach-Mazur games. This characterization is used to prove that, in the sense of Baire category, almost every function in PC[0,1] is nowhere differentiable. This is a complexity-theoretic extension of the analogous classical result that Banach proved for the class C[0, 1] in 1931.

A notion of resource‐bounded Baire category is developed for the classPC[0,1]of all polynomial‐time computable real‐valued functions on the unit interval. The meager subsets ofPC[0,1]are characterized in terms of resource‐bounded Banach‐Mazur games. This characterization is used to prove that, in the sense of Baire category, almost every function inPC[0,1]is nowhere differentiable. This is a complexity‐theoretic extension of the analogous classical result that Banach proved for the classC[0, 1] in 1931. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

We introduce properties of Boolean algebras which are closely related to the existence of winning strategies in the Banach‐Mazur Boolean game. A σ‐short Boolean algebra is a Boolean algebra that has a dense subset in which every strictly descending sequence of length ω does not have a nonzero lower bound. We give a characterization of σ‐short Boolean algebras and study properties of σ‐short Boolean algebras. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim).

We introduce properties of Boolean algebras which are closely related to the existence of winning strategies in the Banach-Mazur Boolean game. A σ-short Boolean algebra is a Boolean algebra that has a dense subset in which every strictly descending sequence of length ω does not have a nonzero lower bound. We give a characterization of σ-short Boolean algebras and study properties of σ-short Boolean algebras.

Banach introduced the following two-person, perfect information, infinite game on the real numbers and asked the question: For which sets $A \subseteq \mathbf{R}$ is the game determined????? Rules: The two players alternate moves starting with player I. Each move a n is legal iff it is a real number and $0 , and for $n > 1, a_n . The first player to make an illegal move loses. Otherwise all moves are legal and I wins iff ∑ a (...) n exists and ∑ a n ∈ A. We will look at this game and some variations of it, called Banach games. In each case we attempt to find the relationship between Banach determinancy and the determinancy of other well-known and much-studied games. (shrink)

This article presents a relatively straightforward theoretical framework about distributive justice with applications. It draws on a few key concepts of Sociological Game Theory. SGT is presented briefly in section 2. Section 3 provides a spectrum of distributive cases concerning principles of equality, differentiation among recipients according to performance or contribution, status or authority, or need. Two general types of social organization of distributive judgment are distinguished and judgment procedures or algorithms are modeled in each type of social organization. (...) Section 4 discusses briefly the larger moral landscapes of human judgment – how distribution may typically be combined with other value into consideration. The article suggests that Rawls, Elster, and Machado point in this direction. Finally, it is suggested that the SGT framework presented provides a useful point of departure to systematically link it and compare the Warsaw School of Fair Division, Rawls, and Elster, among others. (shrink)

We study theorems from Functional Analysis with regard to their relationship with various weak choice principles and prove several results about them: “Every infinite‐dimensional Banach space has a well‐orderable Hamel basis” is equivalent to ; “ can be well‐ordered” implies “no infinite‐dimensional Banach space has a Hamel basis of cardinality ”, thus the latter statement is true in every Fraenkel‐Mostowski model of ; “No infinite‐dimensional Banach space has a Hamel basis of cardinality ” is not provable in ; “No infinite‐dimensional (...) Banach space has a well‐orderable Hamel basis of cardinality ” is provable in ; (the Axiom of Choice for denumerable families of non‐empty finite sets) is equivalent to “no infinite‐dimensional Banach space has a Hamel basis which can be written as a denumerable union of finite sets”; Mazur's Lemma (“If X is an infinite‐dimensional Banach space, Y is a finite‐dimensional vector subspace of X, and, then there is a unit vector such that for all and all scalars α”) is provable in ; “A real normed vector space X is finite‐dimensional if and only if its closed unit ball is compact” is provable in ; (Principle of Dependent Choices) + “ can be well‐ordered” does not imply the Hahn‐Banach Theorem () in ; and “no infinite‐dimensional Banach space has a Hamel basis of cardinality ” are independent from each other in ; “No infinite‐dimensional Banach space can be written as a denumerable union of finite‐dimensional subspaces” lies in strength between (the Axiom of Countable Choice) and ; implies “No infinite‐dimensional Banach space can be written as a denumerable union of closed proper subspaces” which in turn implies ; “Every infinite‐dimensional Banach space has a denumerable linearly independent subset” is a theorem of, but not a theorem of ; and “Every infinite‐dimensional Banach space has a linearly independent subset of cardinality ” implies “every Dedekind‐finite set is finite”. (shrink)

In _The Platonizing Sethian Background of Plotinus’s Mysticism_, Zeke Mazur offers a radical reconceptualization of Plotinus with reference to Gnostic thought and praxis, chiefly as evidenced by Coptic works among the Nag Hammadi Codices whose Greek Vorlagen were read in Plotinus’s school.

We present the notion of finite high-order Gowers games, and prove a statement parallel to Gowers's Combinatorial Lemma for these games. We derive ‘quantitative’ versions of the original Gowers Combinatorial Lemma and of Gowers's Dichotomy, which place them in the context of the recently introduced infinite dimensional asymptotic theory for Banach spaces.

Sur la décomposition des ensembles de points en parties respectivement congruentes.

An alternative proof is given that to each LLM proof net there corresponds at least one LLM sequent proof. The construction is inspired by the sweepline technique from computational geometry and includes a treatment of the multiplicative constants and of proof boxes.

In this paper we give an axiomatisation of the concept of a computability structure with partial sequences on a many‐sorted metric partial algebra, thus extending the axiomatisation given by Pour‐El and Richards in [9] for Banach spaces. We show that every Banach‐Mazur computable partial function from an effectively separable computable metric partial Σ‐algebraAto a computable metric partial Σ‐algebraBmust be continuous, and conversely, that every effectively continuous partial function with semidecidable domain and which preserves the computability of a computably enumerable (...) dense set must be computable. Finally, as an application of these results we give an alternative proof of the first main theorem for Banach spaces first proved by Pour‐El and Richards. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim). (shrink)

This study was designed to determine the quality of service through the evaluation of hospitalized patients. An analysis of hospitalized patients’ subjective feelings towards service quality was carried out, in the context of the application of the SERVQUAL method. The pilot study was conducted in a Silesian hospital in a group of 29 young patients diagnosed with kidney disease. The study used a standard sheet of 22 SERVQUAL statements and an analysis of the significance of the 5 areas of quality (...) material important for the patient. According to the respondents, the most important of the 5 features that influence the quality of life is the ability of the ward staff to provide adequate medical services The least important were the aesthetics and ergonomics of rooms. Service quality gaps were seen in all the five dimensions as well as in the overall service quality. Hence, the following conclusions could be made: 1. The SERVQUAL method helps to identify discrepancies between perceptions of patients’ expectations in all the dimensions of quality of medical services. 2. For patients, the least important is the material dimension, whereas the one most affecting them is the dimension associated with the reliability of medical services. 3. An improvement of the level of satisfaction with the quality of medical services requires proper planning and effectiveness of implementation of health care services. 4. Research should be conducted on a larger population of patients. (shrink)

This article argues that we could improve the design of research protocols by developing an awareness of and a responsiveness to the social contexts of all the actors in the research enterprise, including subjects, investigators, sponsors, and members of the community in which the research will be conducted. ?Social context? refers to the settings in which the actors are situated, including, but not limited to, their social, economic, political, cultural, and technological features. The utility of thinking about social contexts is (...) introduced and exemplified by the presentation of a hypothetical case in which one central issue is limitation of the probability of injury to subjects by selection of individuals who are not expected to live long enough for the known risks of the study to become manifest as harms. Benefits of such considerations may include enhanced subject satisfaction and cooperation, community acceptance, and improved data quality, among other desirable consequences. (shrink)

We demonstrate that social capital is associated with positive food security outcomes, using survey data from 378 households in rural Uganda. We measured food security with the Household Food Insecurity Access Scale. For social capital, we measured cognitive and structural indicators, with principal components analysis used to identify key factors of the concept for logistic regression analysis. Households with bridging and linking social capital, characterized by membership in groups, access to information from external institutions, and observance of norms in groups, (...) tended to be more food secure. Households with cognitive social capital, characterized by observance of generalized norms and mutual trust, were also more food secure than others. However, we established that social capital is, by itself, insufficient. It needs to be complemented with human capital enhancement. We recommend that development interventions which focus on strengthening community associations and networks to enhance food security should support activities which enhance cognitive social capital and human capital skills. Such activities include mutual goal setting, trust building and clear communication among actors. Education efforts for community members, both formal and non-formal, should also be supported such that they potentially strengthen social capital to improve food security in rural Uganda. (shrink)

The aim of our study was to test the effectiveness of the “three good things for others” intervention. We used the randomized controlled trial method, with four measurements (pretest, posttest, follow-up after 2 weeks, follow-up after 4 weeks) and with random assignment of participants to experimental and placebo control groups. We investigated the effects of the intervention on prosocial behavior, and in addition on positive and negative affect, and positive orientation (a general tendency to approach reality in a positive way). (...) The results showed an increase in positive affect and a decrease in negative affect in the experimental group a day after the intervention. These effects, however, did not endure over the next 2 or 4 weeks. We also observed a statistically significant increase in prosocial behavior in the placebo control group, in which participants were engaged in a task of recalling childhood memories. The results are discussed and recommendations for future studies are proposed. (shrink)

In men, high levels of endogenous testosterone (T) seem to encourage behavior intended to dominate other people. Sometimes dominant behavior is aggressive, its apparent intent being to inflict harm on another person, but often dominance is expressed nonaggressively. Sometimes dominant behavior takes the form of antisocial behavior, including rebellion against authority and law breaking. Measurement of T at a single point in time, presumably indicative of a man's basal T level, predicts many of these dominant or antisocial behaviors. T not (...) only affects behavior but also responds to it. The act of competing for dominant status affects male T levels in two ways. First, T rises in the face of a challenge, as if it were an anticipatory response to impending competition. Second, after the competition, T rises in winners and declines in losers. Thus, there is a reciprocity between T and dominance behavior, each affecting the other. We contrast a reciprocal model, in which T level is variable, acting as both a cause and effect of behavior, with a basal model, in which T level is assumed to be a persistent trait that influences behavior. An unusual data set on Air Force veterans, in which data were collected four times over a decade, enables us to compare the basal and reciprocal models as explanations for the relationship between T and divorce. We discuss sociological implications of these models. (shrink)

Hans Morgenthau was a founder of the modern discipline of International Relations, and his Politics among Nations was for decades the dominant textbook in the field. The character of his Realism has frequently been discussed in debates on methodology and the nature of theory in International Relations. Almost all of this discussion has mischaracterized his views. The clues given in his writings, as well as his biography, point directly to Max Weber’s methodological writings. Morgenthau, it is argued, was a sophisticated (...) user of Weber’s views who self-consciously applied them in the sphere of International Relations in such a way that Realism provided an ideal-typical model of the rational and responsible statesman. This interpretation both explains Morgenthau’s views and shows them to be a serious, complex, and compelling response to the issues which have animated the controversies over International Relations theory after Waltz’s presentation of the methodological basis for his neo-Realism. (shrink)

This Response focuses on the strength of the testosterone (T) dominance relationship, the circumstances under which aggression accompanies dominance, the viability of the basal model, mediators and moderators of the T-dominance relationship, and the research that is needed.

The aim of the article is to outline the concept of transcendentalising reduction and to demonstrate what role it plays in Thomistic metaphysics. An adaptive interpretation has been used in the analyses by applying phenomenological thinking based on epoche reduction to Thomistic metaphysics. It was used to present the structure of transcendentalising reduction, which consists of several different epoché. Consistently applied, this reduction should lead to a neutralised concept of being as a subject of metaphysics expressed in the formula “being (...) as being”. In conclusion, we note that the proposed interpretation opens the door to further research in which phenomenology could be used in metaphysical studies to a greater extent than has been the case to date. (shrink)

The most important issue remains: Whether attorneys should serve on HECs? Will they tend to inhibit the development of other discussions, ethical discussions, regarding the issues brought before the HEC? D. Niemira (17, p. 982) suggests that what a hospital needs is not necessarily an attorney to help in their ethical deliberations, but an ethicist. This suggestion should receive further analysis. What types of ethical deliberations to which attorneys have not been exposed in their legal training are important given the (...) broader attorney-role (beyond giving legal opinion) in HEC discussions?The pro-active attorney faces many challenges, both in the current setting (as cases are brought to the HEC) and as future questions are raised (due to innovations in medical technology). These questions remain unclarified by the courts. The nature of the attorney's role is ever challenging; he or she remains in a key position that is currently needed (regarding the uncharted areas of HEC decisionmaking) and important for the future (as new cases emerge and require extensive deliberations). (shrink)