There is a balance between the amount of (weak) indestructibility one can have and the amount of strong cardinals. It’s consistent relative to large cardinals to have lots of strong cardinals and all of their degrees of strength are weakly indestructible. But this necessitates the destructibility of the partially strong cardinals. Guaranteeing the indestructibility of the partially strong cardinals is shown to be harder. In particular, this work establishes an equiconsistency between:

1. 1. a proper class of cardinals that are strong reflecting strongs; and

2. 2. weak indestructibility for (κ+2)-strength for all cardinals κ in the presence of a proper class of strong cardinals.

1. 3. weak indestructibility for all degrees of strength for a proper class of strong cardinals.

One direction of the equiconsistency of (1) and (2) is proven using forcing and the other using core model techniques from inner model theory. Additionally, connections between weak indestructibility and the reflection properties associated with Woodin cardinals are discussed, and similar results are derived for supercompacts and supercompacts reflecting supercompacts.

Abstract prepared by James Holland.

E-mail: jch258@scarletmail.rutgers.edu

URL: https://sites.math.rutgers.edu/~jch258/assets/dis.pdf

We establish an equiconsistency between (1) weak indestructibility for all $\kappa +2$-degrees of strength for cardinals $\kappa $ in the presence of a proper class of strong cardinals, and (2) a proper class of cardinals that are strong reflecting strongs. We in fact get weak indestructibility for degrees of strength far beyond $\kappa +2$, well beyond the next inaccessible limit of measurables (of the ground model). One direction is proven using forcing and the other using core model techniques from inner model theory. Additionally, connections between weak indestructibility and the reflection properties associated with Woodin cardinals are discussed. This work is a part of my upcoming thesis [7].

Among the most controversial reforms investigated by Alexis de Tocqueville and Gustave de Beaumont was the idea of using inheritance as an instrument to diffuse property ownership. This article offers the first comparative account of the development of this concept across each of their major works. By situating their interventions within wider inheritance law debates, it is demonstrated how their evolving visions of democracy forced them to innovatively combine two normative arguments: (i) diffusing property ownership via inheritance was a precondition for placing democracy upon stable political foundations, and (ii) this could counter the rise of pauperism and the extreme wealth inequality of nineteenth-century industrial society. Far from being an anachronistic republican notion, such reforms were long considered too radical to be implemented in England and Ireland.

Social learning is a critical adaptation for dealing with different forms of variability. Uncertainty is a severe form of variability where the space of possible decisions or probabilities of associated outcomes are unknown. We identified four theoretically important sources of uncertainty: temporal environmental variability; payoff ambiguity; selection-set size; and effective lifespan. When these combine, it is nearly impossible to fully learn about the environment. We develop an evolutionary agent-based model to test how each form of uncertainty affects the evolution of social learning. Agents perform one of several behaviours, modelled as a multi-armed bandit, to acquire payoffs. All agents learn about behavioural payoffs individually through an adaptive behaviour-choice model that uses a softmax decision rule. Use of vertical and oblique payoff-biased social learning evolved to serve as a scaffold for adaptive individual learning – they are not opposite strategies. Different types of uncertainty had varying effects. Temporal environmental variability suppressed social learning, whereas larger selection-set size promoted social learning, even when the environment changed frequently. Payoff ambiguity and lifespan interacted with other uncertainty parameters. This study begins to explain how social learning can predominate despite highly variable real-world environments when effective individual learning helps individuals recover from learning outdated social information.

By structuring information in a systematic relational framework, narratives are cultural attractors that are particularly well-suited for transmission. The relational structure of narrative is partly what communicates causality, but this structure also complicates both transmission and selection on cultural elements by introducing correlations among narrative elements and between different narratives. These correlations have implications for adaptation, complexity, and robustness.

Communicating evidence that a policy is effective can increase public support although the effects are small. In the context of policies to increase healthier eating in out-of-home restaurants, we investigate two ways of presenting evidence for a policy's effectiveness: (i) visualising and (ii) re-expressing evidence into a more interpretable form. We conducted an online experiment in which participants were randomly allocated to one of five groups. We used a 2 (text only vs visualisation) × 2 (no re-expression vs re-expression) design with one control group. Participants (n = 4500) representative of the English population were recruited. The primary outcome was perceived effectiveness and the secondary outcome was public support. Evidence of effectiveness increased perceptions of effectiveness (d = 0.14, p < 0.001). There was no evidence that visualising, or re-expressing, changed perceptions of effectiveness (respectively, d = 0.02, p = 0.605; d = −0.02, p = 0.507). Policy support increased with evidence but this was not statistically significant after Bonferroni adjustment (d = 0.08, p = 0.034, α = 0.006). In conclusion, communicating evidence of policy effectiveness increased perceptions that the policy was effective. Neither visualising nor re-expressing evidence increased perceived effectiveness of policies more than merely stating in text that the policy was effective.

Democratic cooperation is a particularly complex type of arrangement that requires attendant institutions to ensure that the problems inherent in collective action do not subvert the public good. It is perhaps due to this complexity that historians, political scientists, and others generally associate the birth of democracy with the emergence of so-called states and center it geographically in the “West,” where it then diffused to the rest of the world. We argue that the archaeological record of the American Southeast provides a case to examine the emergence of democratic institutions and to highlight the distinctive ways in which such long-lived institutions were—and continue to be—expressed by Native Americans. Our research at the Cold Springs site in northern Georgia, USA, provides important insight into the earliest documented council houses in the American Southeast. We present new radiocarbon dating of these structures along with dates for the associated early platform mounds that place their use as early as cal AD 500. This new dating makes the institution of the Muskogean council, whose active participants have always included both men and women, at least 1,500 years old, and therefore one of the most enduring and inclusive democratic institutions in world history.

Linoleic acid (LA), an essential n-6 fatty acid (FA), is critical for fetal development. We investigated the effects of maternal high LA (HLA) diet on offspring cardiac development and its relationship to circulating FA and cardiovascular function in adolescent offspring, and the ability of the postnatal diet to reverse any adverse effects. Female Wistar Kyoto rats were fed low LA (LLA; 1·44 % energy from LA) or high LA (HLA; 6·21 % energy from LA) diets for 10 weeks before pregnancy and during gestation/lactation. Offspring, weaned at postnatal day 25, were fed LLA or HLA diets and euthanised at postnatal day 40 (n 6–8). Maternal HLA diet decreased circulating total cholesterol and HDL-cholesterol in females and decreased total plasma n-3 FA in males, while maternal and postnatal HLA diets decreased total plasma n-3 FA in females. α-Linolenic acid (ALA) and EPA were decreased by postnatal but not maternal HLA diets in both sexes. Maternal and postnatal HLA diets increased total plasma n-6 and LA, and a maternal HLA diet increased circulating leptin, in both male and female offspring. Maternal HLA decreased slopes of systolic and diastolic pressure–volume relationship (PVR), and increased cardiac Col1a1, Col3a1, Atp2a1 and Notch1 in males. Maternal and postnatal HLA diets left-shifted the diastolic PVR in female offspring. Coronary reactivity was altered in females, with differential effects on flow repayment after occlusion. Thus, maternal HLA diets impact lipids, FA and cardiac function in offspring, with postnatal diet modifying FA and cardiac function in the female offspring.

Disease transmission and behaviour change are both fundamentally social phenomena. Behaviour change can have profound consequences for disease transmission, and epidemic conditions can favour the more rapid adoption of behavioural innovations. We analyse a simple model of coupled behaviour change and infection in a structured population characterised by homophily and outgroup aversion. Outgroup aversion slows the rate of adoption and can lead to lower rates of adoption in the later-adopting group or even behavioural divergence between groups when outgroup aversion exceeds positive ingroup influence. When disease dynamics are coupled to the behaviour-adoption model, a wide variety of outcomes are possible. Homophily can either increase or decrease the final size of the epidemic depending on its relative strength in the two groups and on R0 for the infection. For example, if the first group is homophilous and the second is not, the second group will have a larger epidemic. Homophily and outgroup aversion can also produce dynamics suggestive of a ‘second wave’ in the first group that follows the peak of the epidemic in the second group. Our simple model reveals dynamics that are suggestive of the processes currently observed under pandemic conditions in culturally and/or politically polarised populations such as the USA.

Hernando de Soto's expedition through the southeastern United States between 1539 and 1543 is often regarded as a watershed moment for the collapse of Indigenous societies across the region. Historical narratives have proposed that extreme depopulation as a result of early contact destabilized Indigenous economies, politics, networks, and traditions. Although processes of depopulation and transformation were certainly set in motion by this and earlier colonial encounters, the timing, temporality, and heterogeneous rhythms of postcontact Indigenous histories remain unclear. Through the integration of radiocarbon and archaeological data from the Mississippian earthen platform mound at Dyar (9GE5) in central Georgia, we present a case of Indigenous endurance and resilience in the Oconee Valley that has long been obfuscated by materially based chronologies and typologies. Bayesian chronological modeling suggests that Indigenous Mississippian traditions persisted for up to 130 years beyond contact with European colonizers. We argue that advances in modeling radiocarbon dates, along with meaningful consultation/collaboration with descendant communities, can contribute to efforts that move us beyond a reliance on materially based chronologies that can distort and erase Indigenous histories.

The standard theory of rationality posits that agents order preferences according to average utilities associated with different choices. Expected utility theory has repeatedly failed as a predictive theory, as reflected in a growing literature in behavioural economics. Evolutionary theorists have suggested that seemingly irrational behaviours in contemporary contexts may have once served important functions, but existing work linking fitness and choice has not adequately addressed the challenges of constructing an evolutionary theory of decision making. In particular, fitness itself is not a reasonable metric for decision making since its timescale exceeds the lifespan of the decision-maker. Consequently, organisms use proximate systems that work on appropriate timescales and are amenable to feedback and learning. We develop an evolutionary principal–agent model in which individuals utilize a set of proximal choice variables to account for the non-linear dependence of these variables on consumption. While this is insufficient to maximize fitness in the presence of environmental stochasticity, maximum fitness can be achieved by adopting pessimistic probability weightings compatible with the rank-dependent expected utility family of choice models. In particular, pessimistic probability weighting emerges naturally in an evolutionary framework because of extreme intolerance to zeros in multiplicative growth processes.

Parental investment theory predicts that biases in investment favour migration by driving some of the sibling group to disperse for resources. Here we test hypotheses arising from this theory to explain patterns of rural–urban migration in south-central Ethiopia considering familial and individual strategies. We focus on the migration of low-skilled men, predicting two scenarios based on a low level of resource availability. Firstly, last-born sons will be more likely to migrate in order to offset their intra-household disadvantage when resources are limited (sibling competition). Alternatively, in households facing livelihood insecurity, older sons will migrate in order to free resources for their younger dependant brothers (reflecting sibling cooperation). Demographic, economic and relational data were collected from 217 families of male migrants, including information for 830 male adults. We performed multivariate analyses, including Bayesian generalised linear models and mixed models, to analyse quantitative data with a focus on household and individual likelihood of out-migration. Consistent with the predictions from parental investment theory, migration is dependent on intra-household resource allocation. Depending on the stage of the family cycle and livelihood context, families and individuals present different strategies: labour migration may result from sibling competition or from cooperation for resource enhancement.

The endocannabinoid system (ECS), modulated by metabolites of linoleic acid (LA), is important in regulating cardiovascular function. In pregnancy, LA is vital for foetal development. We investigated the effects of elevated LA in H9c2 cardiomyoblasts in vitro and of a high linoleic acid (HLA, 6.21%) or low linoleic acid (LLA, 1.44%) diet during pregnancy in maternal and offspring hearts. H9c2 cell viability was reduced following LA exposure at concentrations between 300 and 1000 µM. HLA diet decreased cannabinoid receptor type 2 (CB2) mRNA expression in foetal hearts from both sexes. However, HLA diet increased CB2 expression in maternal hearts. The mRNA expression of fatty acid amide hydrolase (FAAH) in foetal hearts was higher in females than in males irrespective of diet and N-acyl phosphatidylethanolamine-specific phospholipase D (NAPE-PLD) mRNA expression showed an interaction between diet and sex. Data indicate that a high LA diet alters cell viability and CB2 expression, potentially influencing cardiac function during pregnancy and development of the offspring’s heart.