We study descriptive set theory in the space ω1 ω 1 by letting trees with no uncountable branches play a similar role as countable ordinals in traditional descriptive set theory. By using such trees, we get, for example, a covering property for the class of Π 1 1 -sets of ω1 ω 1 . We call a family U of trees universal for a class V of trees if $\mathscr{U} \subseteq \mathscr{V}$ and every tree in V can be order-preservingly mapped (...) into a tree in U. It is well known that the class of countable trees with no infinite branches has a universal family of size ℵ 1 . We shall study the smallest cardinality of a universal family for the class of trees of cardinality ≤ℵ 1 with no uncountable branches. We prove that this cardinality can be 1 (under ¬CH) and any regular cardinal κ which satisfies ℵ 2 ≤ κ ≤ 2 ℵ 1 (under CH). This bears immediately on the covering property of the Π 1 1 -subsets of the space ω1 ω 1 . We also study the possible cardinalities of definable subsets of ω1 ω 1 . We show that the statement that every definable subset of ω1 ω 1 has cardinality $ or cardinality 2 ω1 is equiconsistent with ZFC (if n ≥ 3) and with ZFC plus an inaccessible (if n = 2). Finally, we define an analogue of the notion of a Borel set for the space ω1 ω 1 and prove a Souslin-Kleene type theorem for this notion. (shrink)

We study descriptive set theory in the space $^{\omega_1}\omega_1$ by letting trees with no uncountable branches play a similar role as countable ordinals in traditional descriptive set theory. By using such trees, we get, for example, a covering property for the class of $\Pi^1_1$-sets of $^{\omega_1}\omega_1$. We call a family $\mathscr{U}$ of trees universal for a class $\mathscr{V}$ of trees if $\mathscr{U} \subseteq \mathscr{V}$ and every tree in $\mathscr{V}$ can be order-preservingly mapped into a tree in $\mathscr{U}$. It is well (...) known that the class of countable trees with no infinite branches has a universal family of size $\aleph_1$. We shall study the smallest cardinality of a universal family for the class of trees of cardinality $\leq\aleph_1$ with no uncountable branches. We prove that this cardinality can be 1 (under $\neg$CH) and any regular cardinal $\kappa$ which satisfies $\aleph_2 \leq \kappa \leq 2^{\aleph_1}$ (under CH). This bears immediately on the covering property of the $\Pi^1_1$-subsets of the space $^{\omega_1}\omega_1$. We also study the possible cardinalities of definable subsets of $^{\omega_1}\omega_1$. We show that the statement that every definable subset of $^{\omega_1}\omega_1$ has cardinality $<\omega_n$ or cardinality $2^{\omega_1}$ is equiconsistent with ZFC (if $n \geq 3$) and with ZFC plus an inaccessible (if $n = 2$). Finally, we define an analogue of the notion of a Borel set for the space $^{\omega_1}\omega_1$ and prove a Souslin-Kleene type theorem for this notion. (shrink)

Contributed research papers chiefly on various aspects of Indic philosophy, Vedic literature, etc.

Contributed research papers chiefly on various aspects of Indic philosophy, Vedic literature, etc.

'This book is a masterpiece of theoretical thought. It anticipates the actual achievements of much of what we now call sociolinguistics.

The association of Berdiaev's name with the phenomenon of perestroika seems strange at first glance and even illogical. But perestroika, which is proceeding—or, more precisely, is trying to proceed—under the sign of an intellectual renaissance, has naturally aroused interest in the names of Russian philosophers who have undeservedly been forgotten. One of these is N.A. Berdiaev . He was a Russian patriot and was profoundly concerned with Russia's fate. Living in a critical period, Berdiaev reflected a great deal over the (...) past, present, and future of his Motherland, advanced the idea of its transformation, and even used the term "perestroika" in doing so. His thoughts concerning Russia's political renewal are profound, and some of them are applicable to the present life of our society. (shrink)

The article analyzes the creativity of one of the most famous Russian neokantians Boris V. Yakovenko. Despite the fact that the work of Yakovenko becomes the subject of analysis of an increasing number of researchers both in Russia and abroad, it has not yet taken place in a systematic analysis. The article attempts to consider the philosophical creativity of the Russian philosopher systematically, revealing both the main directions of European thought that had the greatest influence on the position of Yakovenko (...) and the main areas of philosophy to which the efforts of the national thinker were directed. These, according to the author, include the history of philosophy and the system of so-called transcendental pluralism. It is pointed out that the history of philosophy for Yakovenko is a single holistic process and therefore is the history of the development of philosophical ideas, and not the history of life and work of individual philosophers. According to Yakovenko, the general philosophical scheme of historical development looks like this: from Greek cosmism to German epistemology and the beginning ontological turn in modern philosophy. There is also the belief of B.V. Yakovenko that there is no national philosophy. In his opinion, philosophy, as well as science in General, can only be international. His second main thesis concerning the development of philosophy is that philosophy should be independent from other branches of human knowledge and knowledge. She must not be a servant of theology or science. The article also presents various stages of the Russian philosopher's development of his version of the concept of pluralistic philosophy. According to Yakovenko, only pluralistic philosophy is able to know the essence as the main object of philosophy. (shrink)

Книга предназначена для специалистов в области истории философии, студентов и аспирантов-философов, преподавателей философии и всех интересующихся философией и ее историей.

В форме увлекательных бесед показаны не только высоты и бездны европейской философии, но и значительные достижения русской философской школы, уходящей своими корнями в православное мировосприятие. Для всех, кто хочет научиться серьезно мыслить.

Festschrift in honor of V.N. Jha, b. 1946, Indologist; comprises contributed papers on various aspects of Vedic literature and philosophy.