Consecutive singular cardinals and the continuum function

We show that from a supercompact cardinal \kappa, there is a forcing extension V[G] that has a symmetric inner model N in which ZF + not AC holds, \kappa\ and \kappa^+ are both singular, and the continuum function at \kappa\ can be precisely controlled, in the sense that the final model contains a sequence of distinct subsets of \kappa\ of length equal to any predetermined ordinal. We also show that the above situation can be collapsed to obtain a model of ZF + not AC_\omega\ in which either (1) aleph_1 and aleph_2 are both singular and the continuum function at aleph_1 can be precisely controlled, or (2) aleph_\omega\ and aleph_{\omega+1} are both singular and the continuum function at aleph_\omega\ can be precisely controlled. Additionally, we discuss a result in which we separate the lengths of sequences of distinct subsets of consecutive singular cardinals \kappa\ and \kappa^+ in a model of ZF. Some open questions concerning the continuum function in models of ZF with consecutive singular cardinals are posed.Comment: to appear in the Notre Dame Journal of Formal Logic, issue 54:3, June 201

Singular cardinals and strong extenders

We investigate the circumstances under which there exist a singular cardinal $\mu$ and a short $(\kappa, \mu)$-extender $E$ witnessing "$\kappa$ is $\mu$-strong", such that $\mu$ is singular in \Ult(V, E).Comment: 8 page

The Phenomenon of Suicide Bombing: A Review of Psychological and Nonpsychological Factors

This article reviews the literature on the phenomenon of suicide bombing. It addresses the question of just how much a psychological understanding of the individuals involved can aid in prevention. The article looks at historical, epidemiological, and cultural perspectives and compares the nonpsychological and psychological approaches to suicide bombing. On the basis of the material available it seems that social processes such as group-dynamic indoctrination and political factors are decisive in analyzing this problem. Cultural, nationalistic, and religious factors are important. The conclusion is that in suicidal bombing, suicide is instrumental in the context of war, not in the context of psychopathology. Suicide bombing is instrumental in realizing fatalities, and it is only one of many weapons. The act of killing in warfare is more important to understanding suicidal terrorism than the act of suicide. This explains why psychological profiling of suicidal terrorists has to date not been successful. Keywords: suicide, terror, bombing, indoctrination, psychological and nonpsychological approache