Subcompact cardinals, squares, and stationary reflection

We generalise Jensen's result on the incompatibility of subcompactness with square. We show that alpha^+-subcompactness of some cardinal less than or equal to alpha precludes square_alpha, but also that square may be forced to hold everywhere where this obstruction is not present. The forcing also preserves other strong large cardinals. Similar results are also given for stationary reflection, with a corresponding strengthening of the large cardinal assumption involved. Finally, we refine the analysis by considering Schimmerling's hierarchy of weak squares, showing which cases are precluded by alpha^+-subcompactness, and again we demonstrate the optimality of our results by forcing the strongest possible squares under these restrictions to hold.Comment: 18 pages. Corrections and improvements from referee's report mad

The Machinery of Freedom: Guide to a Radical Capitalism

This book argues the case for a society organized by private property, individual rights, and voluntary co-operation, with little or no government. David Friedman\u27s standpoint, known as \u27anarcho-capitalism\u27, has attracted a growing following as a desirable social ideal since the first edition of The Machinery of Freedom appeared in 1971. This new edition is thoroughly revised and includes much new material, exploring fresh applications of the author\u27s libertarian principles. Among topics covered: how the U.S. would benefit from unrestricted immigration; why prohibition of drugs is inconsistent with a free society; why the welfare state mainly takes from the poor to help the not-so-poor; how police protection, law courts, and new laws could all be provided privately; what life was really like under the anarchist legal system of medieval Iceland; why non-intervention is the best foreign policy; why no simple moral rules can generate acceptable social policies -- and why these policies must be derived in part from the new discipline of economic analysis of law.https://digitalcommons.law.scu.edu/monographs/1006/thumbnail.jp

Path Integrals, Density Matrices, and Information Flow with Closed Timelike Curves

Two formulations of quantum mechanics, inequivalent in the presence of closed timelike curves, are studied in the context of a soluable system. It illustrates how quantum field nonlinearities lead to a breakdown of unitarity, causality, and superposition using a path integral. Deutsch's density matrix approach is causal but typically destroys coherence. For each of these formulations I demonstrate that there are yet further alternatives in prescribing the handling of information flow (inequivalent to previous analyses) that have implications for any system in which unitarity or coherence are not preserved.Comment: 25 pages, phyzzx, CALT-68-188