Forcing with [κ] κ over a model of set theory with a strong partition cardinal, M. Spector produced a generic ultrafilter G on κ such that κ κ /G is not well-founded. Theorem. Let G be Spector-generic over a model M of $ZF + DC + \kappa \rightarrow (\kappa)^\kappa_\alpha, \kappa > \omega$ , for all $\alpha . 1) Every cardinal (well-ordered or not) of M is a cardinal of M[ G]. 2) If A ∈ M[ G] is a well-ordered subset (...) of M, then A ∈ M. Let Φ = κ κ /G. 3) There is an ultrafilter U on Φ such that every member of U has a subset of type Φ, and the intersection of any well-ordered subset of U is in U. 4) Φ satisfies Φ → (Φ) α β for all $\alpha and all ordinals β. 5) There is a linear order Φ' with property 3) above which is not "weakly compact", i.e., $\Phi' \nrightarrow (\Phi')^2$. (shrink)

Following [3], we build higher-order models of analysis resembling the frameworks of nonstandard analysis. The models are entirely canonical, constructed without Choice. Weak transfer principles are developed and the models are applied to topology, graph theory, and measure theory. A Loeb-like measure is constructed.

Following [3], we build higher-order models of analysis resembling the frameworks of nonstandard analysis. The models are entirely canonical, constructed without Choice. Weak transfer principles are developed and the models are applied to topology, graph theory, and measure theory. A Loeb-like measure is constructed.

The paper "Partitions of Products" [DiPH] investigated the polarized partition relation $\begin{pmatrix}\omega\\\omega\\\omega\\\vdots\end{pmatrix} \rightarrow \begin{pmatrix}\alpha_1\\\alpha_1\\\alpha_2\\\vdots \end{pmatrix}$ The relation is consistent relative to an inaccessible cardinal if every α i is finite, but inconsistent if two are infinite. We show here that it consistent (relative to an inaccessible) for one to be infinite. Along the way, we prove an interesting proposition from ZFC concerning partitions of the finite subsets of ω.

Henry M. Sheffer: a bibliography (p. xv-xvi)--Structure: A formulation of the logic of sense and denotation, by A. Church. Notes on the logic of intension, by C.I. Lewis. The logic of terms, by J.W. Miller. Two-valued truth tables for modal functions, by H.S. Leonard. N-valued Boolean algebra, by P. Henle. Triangular matrices determined by two sequences, by L.L. Silverman. The ordered pair in number theory, by W.V. Quine.

DigiCat Publishing presents to you this special edition of "The Evolution of States" by J. M. Robertson. DigiCat Publishing considers every written word to be a legacy of humankind. Every DigiCat book has been carefully reproduced for republishing in a new modern format. The books are available in print, as well as ebooks. DigiCat hopes you will treat this work with the acknowledgment and passion it deserves as a classic of world literature.

Unlike some other reproductions of classic texts (1) We have not used OCR(Optical Character Recognition), as this leads to bad quality books with introduced typos. (2) In books where there are images such as portraits, maps, sketches etc We have endeavoured to keep the quality of these images, so they represent accurately the original artefact. Although occasionally there may be certain imperfections with these old texts, we feel they deserve to be made available for future generations to enjoy.

Excerpt from Rationalism Islam. By the Rt. Hon. Ameer ali syed, of the Judicial Committee of His Majesty's Privy Council, author of The Spirit of Islam and Ethics of Islam. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In (...) rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

The God of Jesus -- The nature of God: an unanswerable question? -- The nature of God in Christian tradition -- And our God?

In this 1974 book a practising scientist and gifted expositor sets forth an exciting point of view on the nature of science and how it works.

Overzicht van de rationalistische traditie in de filosofie van de kunst sinds Kant door een hoogleraar aan de Leuvense universiteit.

"This book contains ideas to develop interdisciplinary and transdisciplinary views on economy and society. It aims to disseminate heterodox ideas on various subjects related to economics and global society. The book is organised in six parts. Part 1 contains the key lectures of Backhaus on the concept of state sciences and of Klamer on the importance of culture for economics. Parts 2- 6 contain successively contributions in the areas of economic paradigms and theories, population and society, corporate issues, environment, and (...) international relations. Examples of the content are: - the changes of family life cycles due to the rise of non-traditional households; - subjective and objective inflation rates after the introduction of the Euro; - the economics of genetic engineering; - the contribution of foreign direct investment to the economic development of host countries; - the inaccuracy of economic models applied in places characterized by extreme income disparities; - the improvement of political and corporate governance; - evolutionary thinking and emission trading; - freedom and order in the European Union; - the reform of social policy in Europe. The book provides interesting creative multi-disciplinary ideas with respect to various topical issues concerning the contemporary global society. It is highly recommended for economists and social scientists in search of broad views on social science and society.". (shrink)