A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0

We partially solve a long-standing problem in the proof theory of explicit mathematics or the proof theory in general. Namely, we give a lower bound of Feferman’s system T0 of explicit mathematics (but only when formulated on classical logic) with a concrete interpretat ion of the subsystem Σ12-AC+ (BI) of second order arithmetic inside T0. Whereas a lower bound proof in the sense of proof-theoretic reducibility or of ordinalanalysis was already given in 80s, the lower bound in the sense of interpretability we give here is new. We apply the new interpretation method developed by the author and Zumbrunnen (2015), which can be seen as the third kind of model construction method for classical theories, after Cohen’s forcing and Krivine’s classical realizability. It gives us an interpretation between classical theories, by composing interpretations between intuitionistic theories

Correlation of the frequencies of Rhesus negative subjects in 65 countries with the mortality rates for nine diseases or disease categories.

<p>The x and y axes show the frequency of Rhesus negative homozygotes in the population of a country and mortality (numbers of deaths per population of 100,000), respectively. The figures represent the results of the Pearson correlation analysis, namely the level of significance (<i>P</i>) and the coefficient of determination, i.e. the fraction of a country’s variability of the specific mortality rate that can be explained by the differences within the frequencies of Rhesus negative subjects.</p

Heterozygote Advantage Probably Maintains Rhesus Factor Blood Group Polymorphism: Ecological Regression Study

<div><p>Rhesus factor polymorphism has been an evolutionary enigma since its discovery in 1939. Carriers of the rarer allele should be eliminated by selection against Rhesus positive children born to Rhesus negative mothers. Here I used an ecologic regression study to test the hypothesis that Rhesus factor polymorphism is stabilized by heterozygote advantage. The study was performed in 65 countries for which the frequencies of RhD phenotypes and specific disease burden data were available. I performed multiple multivariate covariance analysis with five potential confounding variables: GDP, latitude (distance from the equator), humidity, medical care expenditure per capita and frequencies of smokers. The results showed that the burden associated with many diseases correlated with the frequencies of particular Rhesus genotypes in a country and that the direction of the relation was nearly always the opposite for the frequency of Rhesus negative homozygotes and that of Rhesus positive heterozygotes. On the population level, a Rhesus-negativity-associated burden could be compensated for by the heterozygote advantage, but for Rhesus negative subjects this burden represents a serious problem.</p></div

Influence of the stakes on the offers.

<p>Influence of the stakes on the offers.</p

Effect of the amount at stake on the relative proposed shares in the UG.

<p>The stakes are shown on a logarithmic scale and are in CZK. The points were jittered to be better visible in their numbers. Treatment One, where the subjects only answered questions for one amount at stake, is marked with circles and the color of the points and the regression line is blue. The estimated effect size for the influence of the stakes on the shares in Treatment One is 3.2%. Treatment Five, where the subjects answered questions for all five amounts, is marked with squares and it has red points and the regression line. The estimated effect size for the influence of the stakes on the shares in Treatment Five is 3.0%.</p

Mean offers in the DG and the UG.

<p>Mean offers in the DG and the UG.</p

Effect of the amount at stake on the relative proposed shares in the DG.

<p>The stakes are shown on a logarithmic scale and are in CZK. The points were jittered to be better visible in their numbers. Treatment One, where the subjects only answered questions for one amount at stake, is marked with circles and the color of the points and the regression line is blue. The estimated effect size for the influence of the stakes on the shares in Treatment One is 0.8%. Treatment Five, where the subjects answered questions for all five amounts, is marked with squares and it has red points and the regression line. The estimated effect size for the influence of the stakes on the shares in Treatment Five is 1.2%.</p

Effect of the amount at stake on the relative MAOs in the DG.

<p>The stakes are shown on a logarithmic scale and are in CZK. The points were jittered to be better visible in their numbers. Treatment One, where the subjects only answered questions for one amount at stake, is marked with circles and the color of the points and the regression line is blue. The estimated effect size for the influence of the stakes on the shares in Treatment One is 7.5%. Treatment Five, where the subjects answered questions for all five amounts, is marked with squares and it has red points and the regression line. The estimated effect size for the influence of the stakes on the shares in Treatment Five is 1.8%.</p

Descriptive statistics and results of testing differences in personality traits and intelligence between <i>Toxoplasma</i>-infected and <i>Toxoplasma</i>-free RhD-negative and RhD- positive male soldiers.

<p><i>Tau</i> shows effect size and sign, p shows statistical significance measured with partial Kendall tests. Significant results (p<0.05, two-sided test) are printed in bold. <i>Toxoplasma</i>-free and <i>Toxoplasma</i>-infected subjects are coded with 0 and 1, respectively. Therefore, negative Tau means lower test score in <i>Toxoplasma</i> infected subjects. Formal correction for multiple (51) tests was not performed. Theoretically, 2–3 of 51 tests presented in this table should provide false positive results.</p

Correlations of all divergences in health status with gender, hair color, or eye color.

<p>Correlations of all divergences in health status with gender, hair color, or eye color.</p