戦争は悪である。誰もが平和を願う。だがそれにもかかわらず、戦争や軍事には人を魅了するものがある。なぜ人間は「戦い」に惹きつけられるのか?なぜ人は「兵器」に興味を抱くのか?戦争は「純然たる悪意」のみの産 物ではない。むしろ、愛や、希望や、真心や、正義感があるからこそ、人は命をかけて戦うことができ、戦争を正当化できてしまう...。本当に平和について議論をするのならば、軍事は「文化」であり、戦争は「人間的 な営み」であることを、まずは素直に認めなければならない―人間の矛盾と限界を見つめ抜く、挑発的な戦争論。.

本巻は、仏教論理学を存在論、認識論、論理学、真理論、言語哲学の各視点から解説し、さらに全知者・輪廻、刹那滅の論証など、最新の研究成果を通じて、その基本的構造と現代的意義を示す。.

In any nonstandard model of Peano arithmetic, the standard part is not first-order definable. But we show that in some model the standard part is definable as the unique solution of a formula , where P is a unary predicate variable.

We say that a subset A of M is implicitly definable in M if there exists a sentence $\phi$ in the language $\mathcal{L} \cup \{P\}$ such that A is the unique set with $ \models \phi$. We consider implicit definability of subfields of a given field. Among others, we prove the following: $\overline{\mathbb{Q}}$ is not implicitly $\emptyset$-definable in any of its elementary extension $K \succ \overline{\mathbb{Q}}$. $\mathbb{Q}$ is implicitly $\emptyset$-definable in any field K with tr.deg $_{\mathbb{Q}}K < \omega$. In a (...) field extension $\mathbb{Q} < K$ with K algebraically closed, $\mathbb{Q}$ is implicitly definable in K if and only if tr.deg $_{\mathbb{Q}}$ is finite. (shrink)

In this paper we define the notion of -linearity for and discuss interpretability (and noninterpretability) of -linear orders in structures and theories.

We introduce several concepts concerning the indiscernibility of trees. A tree is by definition an ordered set such that, for any a∈O, the initial segment {b∈O:b (...) A of the form η∈O, where O is a tree, and aη labeled by η is an element in M. Such a set A is also called a tree in this paper. We study the indiscernibility of trees A in general settings and apply the obtained results to the study of unstable theories. (shrink)

We consider a problem of constructing a model that omits given complete types. We present two results. The first one is related to the Lopez-Escobar theorem and the second one is a version of Morley's omitting types theorem.

We discuss the possibility of applying the compactness theorem to the study of finite structures. Given a class of finite structures, it is important to determine whether it can be expressed by a particular category of sentences. We are interested in this type of problem, and use nonstandard method for showing the non‐expressibility of certain classes of finite graphs by an existential monadic second order sentence.

In this note we treat maximal and minimal normal subgroups of a superstable group and prove that these groups are definable under certain conditions. Main tool is a superstable version of Zil'ber's indecomposability theorem.

Let T1 and T2 be two simple complete theories in disjoint languages. We prove that there is a simple complete theory which extends T1 ∪ T2 if T2 has a certain condition.

Let M be a model of first order Peano arithmetic and I an initial segment of M that is closed under multiplication. LetM0 be the {0, 1,+}-reduct ofM. We show that there is another model N of PA that is also an expansion of M0 such that a · Ma = a · Na if and only if a ∈ I for all a ∈ M.

We investigate stationarity of types over models in simple theories. In particular, we show that in simple theories with finite SU-rank, any complete type over a model having Cantor-Bendixson rank is stationary.

A theory T is called almost [MATHEMATICAL SCRIPT CAPITAL N]0-categorical if for any pure types p1,…,pn there are only finitely many pure types which extend p1 ∪…∪pn. It is shown that if T is an almost [MATHEMATICAL SCRIPT CAPITAL N]0-categorical theory with I = 3, then a dense linear ordering is interpretable in T.

We introduce a new construction of real closed fields by using an elementary extension of an ordered field with an integer part satisfying. This method can be extend to a finite extension of an ordered field with an integer part satisfying. In general, a field obtained from our construction is either real closed or algebraically closed, so an analogy of Ostrowski's dichotomy holds. Moreover we investigate recursive saturation of an o‐minimal extension of a real closed field by finitely many function (...) symbols. (shrink)

A partial map f of a structure M is called almost total if |M — dom| = |M — ran| < ω. We study a difference between an almost total elementary map and an automorphism.

In this paper, we investigate definable models of Peano Arithmetic PA in a model of PA. For any definable model N without parameters in a model M, we show that N is isomorphic to M if M is elementary extension of the standard model and N is elementarily equivalent to M. On the other hand, we show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M but (...) N is not isomorphic to M. We also show that there is a model M and a definable model N with parameters in M such that N is elementarily equivalent to M, and N is isomorphic to M, but N is not definably isomorphic to M. And also, we give a generalization of Tennenbaum's theorem. At the end, we give a new method to construct a definable model by a refinement of Kotlarski's method. (shrink)

The notion of quasi-minimal structures was defined by B. Zil'ber as a natural generalization of minimal structures. Inspired by his work, we study here basic model theoretic properties of quasiminimal structures. Main result is the construction of ω-saturated quasi-minimal models under ω-stability assumption.

The Asian Logic Conference (ALC) is a major international event in mathematical logic. It features the latest scientific developments in the fields of mathematical logic and its applications, logic in computer science, and philosophical logic. The ALC series also aims to promote mathematical logic in the Asia-Pacific region and to bring logicians together both from within Asia and elsewhere for an exchange of information and ideas. This combined proceedings volume represents works presented or arising from the 14th and 15th ALCs.

We study generalized amalgamation properties in simple theories. We formulate a notion of generalized amalgamation in such a way so that the properties are preserved when we pass from T to Teq or Theq; we provide several equivalent ways of formulating the notion of generalized amalgamation.We define two distinct hierarchies of simple theories characterized by their amalgamation properties; examples are given to show the difference between the hierarchies.

Let L be a finite relational language and α=(αR:R ∈ L) a tuple with 0 < αR ≤1 for each R ∈ L. Consider a dimension function $ \delta _\alpha (A) = \left| A \right| - \sum\limits_{R \in L} {\alpha {\mathop{\rm Re}\nolimits} R(A)} $ where each eR(A) is the number of realizations of R in A. Let $K_\alpha $ be the class of finite structures A such that $\delta _\alpha (X) \ge 0$ 0 for any substructure X of A. We (...) show that the theory of the generic model of $K_\alpha $ is AE-axiomatizable for any α. (shrink)

We study model companions of theories extending the graph axioms. First we prove general results concerning the existence of the model companion. Then, by applying these results to the case of graphs, we give a series of companionable and non‐companionable examples.

An Introduction to Buddhism. Jikido Takasaki; tr. by Rolf W. Giebel. The Toho Gakkai, Tokyo 1987. ix, 376 pp. Yen 6000.

In modern Buddhist scholarship, J. Takasaki’s English and Japanese translations of the Ratnagotravibhāga in 1966 and 1989 have been read as an exemplary one until now without any meaningful revision. This paper critically reviews his translations of the twenty-seventh verse in the first chapter of the work, which explicates the key doctrine in the Tathāgatagarbha thought that every living being is a tathāgatagarbha. The method is to clarify the ambiguity of expressions appeared in the verse by changing its nominal (...) style into a general one. After resolving the problems that occur due to vague phrasing, it attempts to investigate the doctrine on the basis of the concepts of buddhakāya, tathatā and gotra, which respectively consist in the first, the second, and the third pāda of the twenty-seventh verse. This paper, thus, provides a new translation of the verse: “Since the Buddha’s wisdom is inherent in all living beings; since the immaculateness of living beings and that of the Buddha are essentially non-dual; and since a buddha is figuratively expressed to be the effect of the buddha-nature with which all living beings are endowed; all body-possessors [=living beings] are by their nature buddhas.”. (shrink)