Let λ denote a singular cardinal. Zeman, improving a previous result of Shelah, proved that $\square _{\lambda}^{\ast}$ together with 2 λ = λ⁺ implies $\lozenge _{S}$ for every S ⊆ λ⁺ that reflects stationarily often. In this paper, for a set S ⊆ λ⁺, a normal subideal of the weak approachability ideal is introduced, and denoted by I[S; λ]. We say that the ideal is fat if it contains a stationary set. It is proved: 1. if I[S; λ] is (...) fat, then $\text{NS}_{\lambda ^{+}}$ ↾ S is non-saturated; 2. if I[S; λ] is fat and 2 λ = λ⁺, then $\lozenge _{S}$ holds; 3. $\square _{\lambda}^{\ast}$ implies that I[S; λ] is fat for every S ⊆ λ⁺ that reflects stationarily often; 4. it is relatively consistent with the existence of a supercompact cardinal that $\square _{\lambda}^{\ast}$ fails, while I[S; λ] is fat for every stationary S ⊆ λ⁺ that reflects stationarily often. The stronger principle $\lozenge _{\lambda ^{+}}^{\ast}$ is studied as well. (shrink)

In the reported, experiment participants hit a ball to aim at the vertex of a Müller–Lyer configuration. This configuration either remained stable, changed its shaft length or the orientation of the tails during movement execution. A significant illusion bias was observed in all perturbation conditions, but not in the stationary condition. The illusion bias emerged for perturbations shortly after movement onset and for perturbations during execution, the latter of which allowed only a minimum of time for making adjustments . (...) These findings indicate that allocentric information is exploited for online control when people make rapid adjustments in response to a sudden change in the environment and not when people guide their limb movements to interact with a stable environment. (shrink)

In an article published in 1974, Menas conjectured that any stationary subset of can be split in many pairwise disjoint stationary subsets. Even though the conjecture was shown long ago by Baumgartner and Taylor to be consistently false, it is still haunting papers on. In which situations does it hold? How much of it can be proven in ZFC? We start with an abridged history of the conjecture, then we formulate a new version of it, and finally we (...) keep weakening this new assertion until, building on the work of Usuba, we hit something we can prove. (shrink)

Study on religious communities honesty as ethics derived from relions in Thailand.

In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal $\nu $ such that the singular cardinal hypothesis fails at $\nu $ and every collection of fewer than $\operatorname {\mathrm {cf}}(\nu )$ stationary subsets of $\nu ^{+}$ reflects simultaneously. For $\operatorname {\mathrm {cf}}(\nu )> \omega $, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation (...) for $\operatorname {\mathrm {cf}}(\nu ) = \omega $ to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon. (shrink)

We characterize the (κ, Λ, < μ)-distributive law in Boolean algebras in terms of cut and choose games $\scr{G}_{<\mu}^{\kappa}(\lambda)$ , when μ ≤ κ ≤ Λ and κ<κ = κ. This builds on previous work to yield game-theoretic characterizations of distributive laws for almost all triples of cardinals κ, Λ, μ with μ ≤ Λ, under GCH. In the case when μ ≤ κ ≤ Λ and κ<κ = κ, we show that it is necessary to consider whether the κ-stationarity (...) of Pκ+Λ in the ground model is preserved by B. In this vein, we develop the theory of κ-club and κ-stationary subsets of Pκ+Λ. We also construct Boolean algebras in which Player I wins $\scr{G}_{\kappa}^{\kappa}(\kappa ^{+})$ but the (κ, ∞, κ)-d.1, holds, and, assuming GCH, construct Boolean algebras in which many games are undetermined. (shrink)

We prove that the statement "For every pair A, B, stationary subsets of ω 2 , composed of points of cofinality ω, there exists an ordinal α such that both A ∩ α and $B \bigcap \alpha$ are stationary subsets of α" is equiconsistent with the existence of weakly compact cardinal. (This completes results of Baumgartner and Harrington and Shelah.) We also prove, assuming the existence of infinitely many supercompact cardinals, the statement "Every stationary subset of ω (...) ω + 1 has a stationary initial segment.". (shrink)

Let A be a non-empty set. A set $S\subseteq \mathcal{P}(A)$ is said to be stationary in $\mathcal{P}(A)$ if for every f: [A] <ω → A there exists x ∈ S such that x ≠ A and f"[x] <ω ⊆ x. In this paper we prove the following: For an uncountable cardinal λ and a stationary set S in \mathcal{P}(\lambda) , if there is a regular uncountable cardinal κ ≤ λ such that {x ∈ S: x ⋂ κ ∈ (...) κ} is stationary, then S can be split into κ disjoint stationary subsets. (shrink)

REF is the statement that every stationary subset of a cardinal reflects, unless it fails to do so for a trivial reason. The main theorem, presented in Sect. 0, is that under suitable assumptions it is consistent that REF and there is a κ which is κ+n -supercompact. The main concepts defined in Sect. 1 are PT, which is a certain statement about the existence of transversals, and the “bad” stationary set. It is shown that supercompactness (and even (...) the failure of PT) implies the existence of non-reflecting stationary sets. E.g., if REF then for manyλ ⌝ PT(λ, ℵ1). In Sect. 2 it is shown that Easton-support iteration of suitable Levy collapses yield a universe with REF if for every singular λ which is a limit of supercompacts the bad stationary set concentrates on the “right” cofinalities. In Sect. 3 the use of oracle c.c. (and oracle proper—see [Sh-b, Chap. IV] and [Sh 100, Sect. 4]) is adapted to replacing the diamond by the Laver diamond. Using this, a universe as needed in Sect. 2 is forced, where one starts, and ends, with a universe with a proper class of supercompacts. In Sect. 4 bad sets are handled in ZFC. For a regular λ {δ<+ : cfδ<λ} is good. It is proved in ZFC that ifλ=cfλ>ℵ1 then {α<+ : cfα<λ} is the union of λ sets on which there are squares. (shrink)

This paper will define a new cardinal called aStationary Cardinal. We will show that every weakly∏ 1 1 -indescribable cardinal is a stationary cardinal, every stationary cardinal is a greatly Mahlo cardinal and every stationary set of a stationary cardinal reflects. On the other hand, the existence of such a cardinal is independent of that of a∏ 1 1 -indescribable cardinal and the existence of a cardinal such that every stationary set reflects is also independent (...) of that of a stationary cardinal. As applications, we will show thatV=L implies ◊ κ 1 holds if κ is∏ 1 1 -indescribable and so forth. (shrink)

We investigate the relationship between weak square principles and simultaneous reflection of stationary sets.

Understanding how transcription factor (TF) binding is related to gene regulation is a moving target. We recently uncovered genome‐wide evidence for a “Hit‐and‐Run” model of transcription. In this model, a master TF “hits” a target promoter to initiate a rapid response to a signal. As the “hit” is transient, the model invokes recruitment of partner TFs to sustain transcription over time. Following the “run”, the master TF “hits” other targets to propagate the response genome‐wide. As such, a TF may act (...) as a “catalyst” to mount a broad and acute response in cells that first sense the signal, while the recruited TF partners promote long‐term adaptive behavior in the whole organism. This “Hit‐and‐Run” model likely has broad relevance, as TF perturbation studies across eukaryotes show small overlaps between TF‐regulated and TF‐bound genes, implicating transient TF‐target binding. Here, we explore this “Hit‐and‐Run” model to suggest molecular mechanisms and its biological relevance. (shrink)

Working in the context of restricted forms of the Axiom of Choice, we consider the problem of splitting the ordinals below λ of cofinality θ into λ many stationary sets, where θ < λ are regular cardinals. This is a continuation of [4].

We characterize the -distributive law in Boolean algebras in terms of cut and choose games.

Transcriptional silencing may not necessarily depend on the continuous residence of a sequence‐specific repressor at a control element and may act via a “hit and run” mechanism. Due to limitations in assays that detect transcription factor (TF) binding, such as chromatin immunoprecipitation followed by high‐throughput sequencing (ChIP‐seq), this phenomenon may be challenging to detect and therefore its prevalence may be underappreciated. To explore this possibility, erythroid gene promoters that are regulated directly by GATA1 in an inducible system are analyzed. It (...) is found that many regulated genes are bound immediately after induction of GATA1 but the residency of GATA1 decreases over time, particularly at repressed genes. Furthermore, it is shown that the repressive mark H3K27me3 is seldom associated with bound repressors, whereas, in contrast, the active (H3K4me3) histone mark is overwhelmingly associated with TF binding. It is hypothesized that during cellular differentiation and development, certain genes are silenced by repressive TFs that subsequently vacate the region. Catching such repressor TFs in the act of silencing via assays such as ChIP‐seq is thus a temporally challenging prospect. The use of inducible systems, epitope tags, and alternative techniques may provide opportunities for detecting elusive “hit and run” transcriptional silencing. Also see the video abstract here https://youtu.be/vgrsoP_HF3g. (shrink)

In this paper, we investigate the dynamics of autonomous and nonautonomous stochastic toxin-producing phytoplankton–zooplankton system. For the autonomous system, we establish the sufficient conditions for the existence of the globally positive solution as well as the solution of population extinction and persistence in the mean. Furthermore, by constructing some suitable Lyapunov functions, we also prove that there exists a single stationary distribution which is ergodic, what is more important is that Lyapunov function does not depend on existence and stability (...) of equilibrium. For the nonautonomous periodic system, we prove that there exists at least one nontrivial positive periodic solution according to the theory of Khasminskii. Finally, some numerical simulations are introduced to illustrate our theoretical results. The results show that weaker white noise and/or toxicity will strengthen the stability of system, while stronger white noise and/or toxicity will result in the extinction of one or two populations. (shrink)

The stationary set splitting game is a game of perfect information of length ω1 between two players, unsplit and split, in which unsplit chooses stationarily many countable ordinals and split tries to continuously divide them into two stationary pieces. We show that it is possible in ZFC to force a winning strategy for either player, or for neither. This gives a new counterexample to Σ22 maximality with a predicate for the nonstationary ideal on ω1, and an example of (...) a consistently undetermined game of length ω1 with payoff de.nable in the second-order monadic logic of order. We also show that the determinacy of the game is consistent with Martin's Axiom but not Martin's Maximum. (shrink)

We study the structural rainbow Ramsey theory at uncountable cardinals. Compared to the usual rainbow Ramsey theory, the variation focuses on finding a rainbow subset that not only is of a certain cardinality but also satisfies certain structural constraints, such as being stationary or closed in its supremum. In the process of dealing with cardinals greater than ω1, we uncover some connections between versions of Chang's Conjectures and instances of rainbow Ramsey partition relations, addressing a question raised in [18].

We improve the upper bound for the consistency strength of stationary reflection at successors of singular cardinals.

Traditionally, identity and supervenience have been proposed in philosophy of mind as metaphysical accounts of how mental activities (fully understood, as they might be at the end of science) relate to brain processes. Kievet et al. suggest that to be relevant to cognitive neuroscience, these philosophical positions must make empirically testable claims and be evaluated accordingly – they cannot sit on the sidelines, awaiting the hypothetical completion of cognitive neuroscience. We agree with the authors on the importance of rendering these (...) positions relevant to ongoing science. We disagree, however, with their proposal that a metaphysical relationship (identity or supervenience) should “serve as a means to conceptually organize and guide the analysis of neurological and behavioral data” (p. 7). Instead, we advance a different view of the goals of cognitive neuroscience and of the proper means of relating metaphysics and explanation. Our central objection to the psychometric approach deployed by Kievet et al. is that the formal models only account for correlations between variables (measurements) and do not aid in explaining phenomena. Cognitive neuroscience is concerned with the latter. We develop this point in section 2 in which we present what we find to be problematic in their proposed models. In section 3 we advance an account of what is required to explain phenomena: (a) providing an adequate description of a phenomenon; and (b) characterizing the mechanism responsible for it. In doing so we will characterize a version of the identity theory, heuristic identity theory (HIT) which figures centrally in developing such explanations and illustrate its role in what we take to.. (shrink)

This paper employs a case study from the history of neuroscience—brain reward function—to scrutinize the inductive argument for the so-called ‘Heuristic Identity Theory’ (HIT). The case fails to support HIT, illustrating why other case studies previously thought to provide empirical support for HIT also fold under scrutiny. After distinguishing two different ways of understanding the types of identity claims presupposed by HIT and considering other conceptual problems, we conclude that HIT is not an alternative to the traditional identity theory so (...) much as a relabeling of previously discussed strategies for mechanistic discovery. (shrink)

A key challenge for understanding transcriptional regulation is being able to measure transcription factor (TF)‐DNA binding events with sufficient spatial and temporal resolution; that is, when and where TFs occupy their cognate sites. A recent study by Para et al. has highlighted the dynamics underlying the activation of gene expression by a master regulator TF. This study provides concrete evidence for a long‐standing hypothesis in biology, the “hit‐and‐run” mechanism, which was first proposed decades ago. That is, gene expression is dynamically (...) controlled by a TF that transiently binds and activates a target gene, which might stay in a transcriptionally active state after the initial binding event has ended. Importantly, the experimental procedure introduced, TARGET, provides a useful way for identifying multiple target genes transiently bound by their regulators, which can be used in conjunction with other well‐established methods to improve our understanding of transcriptional regulatory dynamics. (shrink)

The trolley problem is one of the liveliest research frameworks in experimental ethics. In the last decade, social neuroscience and experimental moral psychology have gone beyond the studies with mere text-based hypothetical moral dilemmas. In this article, I present the rationale behind testing the actual behaviour in more realistic scenarios through Virtual Reality and summarize the body of evidence raised by the experiments with virtual trolley scenarios. Then, I approach the argument of Ramirez and LaBarge (2020), who claim that the (...) virtual simulation of the Footbridge version of the trolley dilemma is an unethical research practice, and I raise some objections to it. Finally, I provide some reflections about the means and ends of trolley-like scenarios and other sacrificial dilemmas in experimental ethics. (shrink)

Current research in set theory raises the possibility that \ can be made compatible with some stationary reflection, depending on the parameter \. The purpose of this paper is to demonstrate the difficulty in such results. We prove that the poset \\), which adds a \-sequence by initial segments, will also add non-reflecting stationary sets concentrating in any given cofinality below \. We also investigate the CMB poset, which adds \ in a slightly different way. We prove that (...) the CMB poset also adds non-reflecting stationary sets, but not necessarily concentrating in any cofinality. (shrink)

A tissue is a geometrical, space-filling, random cellular network; it remains in this steady state while individual cells divide. Cell division is a local, elementary topological transformation which establishes statistical equilibrium of the structure. We describe the physical conditions to maintain stationary the epidermis (of mammals or of the cucumber), in spite of the fact that cells constantly divide and die. Specifically, we study the statistical equilibrium of the basal layer, a corrugated surface filled with cells, constituting a two-dimensional (...) topological froth. Cells divide and detach from the basal layer, and these two topological transformations are responsible for the stationary state of the epidermis. The topological froth is capable of responding rapidly and locally to external constraints, and is a good illustration of the plasticity of random cellular networks.Statistical equilibrium is controlled by entropy, both as a measure of disorder and as information, and is characterized by observable relations between average cell shapes and sizes. The technique can be applied to any random cellular network in dynamical equilibrium. Mitosis as the dominating topological transformation and the fact that the distribution of cell shapes is very narrow are the only inputs specific to biology. (shrink)

Meinong had problems with reality: when having an experience, one cannot tell whether its object is real or not. The problem surfaced in many contexts but it was always connected with the notion of presentation {Vorstellung). This concept, as used in the Austrian phenomenological tradition, is ambiguous: a presentation can be (1) the neutral content that is a part of any mental act, or (2) the act of mere presentation, i.e. the combination of a content and the psychological mode of (...) mere entertaining, or (3) the act of perceiving a simple object.Meinong's pupil France Veber first adopted an orthodox Meinongian view of presentation but later he became aware of the problems connected with it. He argued that there are mental acts in which the subject is in direct contact with reahty or, as he put it, "hits" reality. Thus, acts of perception have two functions, those of presenting and "hitting".It is argued, first, that there are interesting parallels between Veber's concept of zadevanje Chitting') and modem theories of direct mental reference, de re acts and indexicality; and second, that although Veber correctly saw the problem, his solution is not quite satisfactory, because he thought that one has to abandon phenomenology (or the theory of objects) in order to account for the experience of hitting reality. A thoroughly phenomenological theory of „hitting" may be possible, after all. (shrink)

Meinong had problems with reality: when having an experience, one cannot tell whether its object is real or not. The problem surfaced in many contexts but it was always connected with the notion of presentation {Vorstellung). This concept, as used in the Austrian phenomenological tradition, is ambiguous: a presentation can be (1) the neutral content that is a part of any mental act, or (2) the act of mere presentation, i.e. the combination of a content and the psychological mode of (...) mere entertaining, or (3) the act of perceiving a simple object.Meinong's pupil France Veber first adopted an orthodox Meinongian view of presentation but later he became aware of the problems connected with it. He argued that there are mental acts in which the subject is in direct contact with reahty or, as he put it, "hits" reality. Thus, acts of perception have two functions, those of presenting and "hitting".It is argued, first, that there are interesting parallels between Veber's concept of zadevanje Chitting') and modem theories of direct mental reference, de re acts and indexicality; and second, that although Veber correctly saw the problem, his solution is not quite satisfactory, because he thought that one has to abandon phenomenology (or the theory of objects) in order to account for the experience of hitting reality. A thoroughly phenomenological theory of „hitting" may be possible, after all. (shrink)

This chapter contains sections titled: Aisha's Coming Out The Legal Controversy Understanding the Context Violence Physical Violence Phenomenological Violence Epistemic Violence Aisha's Crossing Over Notes.

In this book, Peter Szendy probes the ever-growing and ever more global phenomenon of the hit song.

We introduce three families of diagonal reflection principles for matrices of stationary sets of ordinals. We analyze both their relationships among themselves and their relationships with other known principles of simultaneous stationary reflection, the strong reflection principle, and the existence of square sequences.

We study the relationship between the semistationary reflection principle and stationary reflection principles. We show that for all regular cardinals Λ ≥ ω₂ the semistationary reflection principle in the space [Λ](1) implies that every stationary subset of $E_{\omega}^{\lambda}\coloneq \{\alpha \in \lambda \,|\,{\rm cf}(\alpha)=\omega \}$ reflects. We also show that for all cardinals Λ ≥ ω₃ the semistationary reflection principle in [Λ](1) does not imply the stationary reflection principle in [Λ](1).

We obtain an array of consistency results concerning trees and stationary reflection at double successors of regular cardinals $\kappa $, updating some classical constructions in the process. This includes models of $\mathsf {CSR}(\kappa ^{++})\wedge {\sf TP}(\kappa ^{++})$ (both with and without ${\sf AP}(\kappa ^{++})$ ) and models of the conjunctions ${\sf SR}(\kappa ^{++}) \wedge \mathsf {wTP}(\kappa ^{++}) \wedge {\sf AP}(\kappa ^{++})$ and $\neg {\sf AP}(\kappa ^{++}) \wedge {\sf SR}(\kappa ^{++})$ (the latter was originally obtained in joint work by Krueger (...) and the first author [9], and is here given using different methods). Analogs of these results with the failure of $\sf {SH}(\kappa ^{++})$ are given as well. Finally, we obtain all of our results with an arbitrarily large $2^\kappa $, applying recent joint work by Honzik and the third author. (shrink)

We introduce the notion of skinniness for subsets of $\mathcal{P}_\kappa \lambda$ and its variants, namely skinnier and skinniest. We show that under some cardinal arithmetical assumptions, precipitousness or $2^\lambda$-saturation of $\mathrm{NS}_{\kappa\lambda}\mid X$, where $\mathrm{NS}_{\kappa\lambda}$ denotes the non-stationary ideal over $\mathcal{P}_\kappa \lambda$, implies the existence of a skinny stationary subset of $X$. We also show that if $\lambda$ is a singular cardinal, then there is no skinnier stationary subset of $\mathcal{P}_\kappa \lambda$. Furthermore, if $\lambda$ is a strong limit (...) singular cardinal, there is no skinny stationary subset of $\mathcal{P}_\kappa \lambda$. Combining these results, we show that if $\lambda$ is a strong limit singular cardinal, then $\mathrm{NS}_{\kappa\lambda}\mid X$ can satisfy neither precipitousness nor $2^\lambda$-saturation for every stationary $X \subseteq \mathcal{P}_\kappa \lambda$. We also indicate that $\diamondsuit_\lambda(E^{\lambda}_{<\kappa})$, where $E^{\lambda}_{<\kappa} \stackrel{\mathrm{def}}{=} \{\alpha < \lambda \mid \mathrm{cf}(\alpha) < \kappa\}$, is equivalent to the existence of a skinnier (or skinniest) stationary subset of $\mathcal{P}_\kappa \lambda$ under some cardinal arithmetical hypotheses. (shrink)

For a regular cardinal κ with κ<κ = κ and κ ≤ λ , we construct generically a subset S of {x ∈ Pκλ : x ∩ κ is a singular ordinal} such that S is stationary in a strong sense but the stationarity of S can be destroyed by a κ+-c. c. forcing ℙ* which does not add any new element of Pκλ . Actually ℙ* can be chosen so that ℙ* is κ-strategically closed. However we show that (...) such ℙ* itself cannot be κ-strategically closed or even <κ-strategically closed if κ is inaccessible. (shrink)

We present a variety of (ω 1 ,∞)-distributive forcings which when applied to models of Martin's Maximum separate certain well known reflection principles. In particular, we do this for the reflection principles SR, SR α (α ≤ ω 1 ), and SRP.

Following the general formalism presented by Rezzolla, Ahmedov and Miller, (1) we here derive analytic solutions of the electromagnetic fields equations in the internal and external background spacetime of a slowly rotating highly conducting magnetized neutron star. The star is assumed to be isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. Our results indicate that the electromagnetic fields of a slowly rotating neutron star are modified by general relativistic effects arising from both (...) the monopolar and the dipolar parts of the gravitational field. The results presented here differ from the ones discussed by Rezzolla, Ahmedov and Miller (1) mainly in that we here consider the interior magnetic field to be dipolar with the same radial dependence as the external one. While this assumption might not be a realistic one, it should be seen as the application of our formalism to a case often discussed in the literature. (shrink)

Let κ denote a regular uncountable cardinal and NS the normal ideal of nonstationary subsets of κ. Our results concern the well-known open question whether NS fails to be κ + -saturated, i.e., are there κ + stationary subsets of κ with pairwise intersections nonstationary? Our first observation is: Theorem. NS is κ + -saturated iff for every normal ideal J on κ there is a stationary set $A \subseteq \kappa$ such that $J = NS \mid A = (...) \{X \subseteq \kappa:X \cap A \in NS\}$ . Turning our attention to large cardinals, we extend the usual (weak) Mahlo hierarchy to define "greatly Mahlo" cardinals and obtain the following: Theorem. If κ is greatly Mahlo then NS is not κ + -saturated. Theorem. If κ is ordinal Π 1 1 -indescribable (e.g., weakly compact), ethereal (e.g., subtle), or carries a κ-saturated ideal, then κ is greatly Mahlo. Moreover, there is a stationary set of greatly Mahlo cardinals below any ordinal Π 1 1 -indescribable cardinal. These methods apply to other normal ideals as well; e.g., the subtle ideal on an ineffable cardinal κ is not κ + -saturated. (shrink)

This chapter contains sections titled: Of Jerks and “Nice” Guys Gurus of The Game Aristotle: My Wingman After The Game.

Since the work of Gödel and Cohen, which showed that Hilbert's First Problem was independent of the usual assumptions of mathematics, there have been a myriad of independence results in many areas of mathematics. These results have led to the systematic study of several combinatorial principles that have proven effective at settling many of the important independent statements. Among the most prominent of these are the principles diamond and square discovered by Jensen. Simultaneously, attempts have been made to find suitable (...) natural strengthenings of ZFC, primarily by Large Cardinal or Reflection Axioms. These two directions have tension between them in that Jensen's principles, which tend to suggest a rather rigid mathematical universe, are at odds with reflection properties. A third development was the discovery by Shelah of "PCF Theory", a generalization of cardinal arithmetic that is largely determined inside ZFC. In this paper we consider interactions between these three theories in the context of singular cardinals, focusing on the various implications between square and scales, and on consistency results between relatively strong forms of square and stationary set reflection. (shrink)

There is a strong impetus in international agricultural development to close ‘gender gaps’ in agricultural productivity. The goal of empowering women is often framed as the solution to closing these gaps, stimulating the proliferation of new indicators and instruments for the targeting, measurement, and tracking of programmatic goals in research for agricultural development. Despite these advances, current measurements and indices remain too simplified in terms of unit and scope of analysis, as well as being fundamentally flawed in how they aim (...) to capture the relevance of ‘gender’ in diverse local contexts. We propose that the impulse to apply exogenously defined and weakly validated ‘women’s empowerment’ measures to diverse local contexts risks prioritizing practical expedience over scientific accuracy and societal relevance. Furthermore, the application of such measures risks creating the impression that programmatic “gender targets” are being achieved, while simultaneously undermining substantive gender transformative goals. The authors conclude that a different methodological approach grounded in participatory and qualitative methods is needed to create more meaningful metrics for assessing progress towards women’s empowerment. (shrink)

In this paper, assuming large cardinals, we prove the consistency of the following: Let n ∈ ω and k1, k2 ≤ n. Let f: ω → {k1, k2} be such that for all $n_1 n, cf(\mathscr{B} \cap \omega_m) = \omega_{f(m)}$.

From 1953 to 1959 Gödel worked on a response to Carnap’s philosophy of mathematics. The drafts display Gödel’s familiarity with Carnap’s position from The Logical Syntax of Language, but they received a dismissive reaction on their eventual, posthumous, publication. Gödel’s two principal points, however, will here be defended. Gödel, though, had wished simply to append a few paragraphs to show that the same arguments apply to Carnap’s later views. Carnap’s position, however, had changed significantly in the intervening years, and to (...) a significant extent, this mature position realizes much of what Gödel himself wanted out of a philosophy of mathematics. (shrink)