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.

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。.

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.

"Deep Words contains translations of "Honso, the "Core Text" of "Gengo, by Miura Baien, 1723-1789 - a widely renowned Japanese teacher and writer of his time; ...

Peptides possessing both natriuretic and smooth muscle relaxant activities have been isolated from heart atria and their structures have been determined. The peptides designated ANP (atrial natriuretic peptide) regulate salt and water balance and blood pressure. The scope of this article is to provide a summary of recent research developments directed towards understanding the molecular nature of atrial natriuretic peptides.

ABSTRACTWe tested the response dynamics of the evaluative priming effect using a mouse tracking procedure that records hand movements during the execution of categorisation tasks. In Experiment 1, when participants performed the evaluative categorisation task but not the non-evaluative semantic categorisation task, their mouse trajectories for evaluatively incongruent trials curved more toward the opposite response than those for evaluatively congruent trials, indicating the emergence of evaluative priming effects based on response competition. In Experiment 2, implementing a task-switching procedure in which (...) evaluative and non-evaluative categorisation tasks were intermixed, we obtained reliable evaluative priming effects in the non-evaluative semantic categorisation task as well as in the evaluative categorisation task when participants assigned attention to the evaluative stimulus dime... (shrink)

In motion-induced blindness , a target within rotating random dots is occasionally hidden from observers’ consciousness during observation. In the present study, a red ring-like cue was centered on a target and presented immediately after observers reported subjective disappearance of the target in MIB . The radius of the cue was systematically modulated. Observers quickly regained awareness of the disappeared object only after they were provided with a pinpoint cue of its location. We also found that a flickering cue at (...) 1 Hz hindered MIB when the radius of the cue was critically small . Furthermore, abrupt onset of a small square was enough to regain awareness of the target . Successful revival of the target with a small cue indicates that critical spatial distribution of visual attention determines what in the visual scene is included in visual awareness. (shrink)

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.

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 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 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.

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)

Alternative cleavage and polyadenylation (APA) can diversify coding and non‐coding regions, but has particular impact on increasing 3′ UTR diversity. Through the gain or loss of regulatory elements such as RNA binding protein and microRNA sites, APA can influence transcript stability, localization, and translational efficiency. Strikingly, the central nervous systems of invertebrate and vertebrate species express a broad range of transcript isoforms bearing extended 3′ UTRs. The molecular mechanism that permits proximal 3′ end bypass in neurons is mysterious, and only (...) beginning to be elucidated. This landscape of neural 3′ UTR extensions, many reaching unprecedented lengths, may help service the unique post‐transcriptional regulatory needs of neurons. A combination of approaches, including transcriptome‐wide profiling, genetic screening to identify APA factors, biochemical dissection of alternative 3′ end formation, and manipulation of individual neural APA targets, will be necessary to gain fuller perspectives on the mechanism and biology of neural‐specific 3′ UTR lengthening. (shrink)

Biological forms are very complex, and mechanisms of pattern formation are not well understood. Although developmental biology deals with the mechanistic explanation of patterns, currently we do not know how to understand the mechanisms of pattern formation from huge amounts of molecular information. In this article, I present one useful tool, mathematical modeling, to obtain a mechanistic understanding of biological pattern formation, and show an actual example in lung branching morphogenesis. In this example, mathematical modeling plays an indispensable role in (...) understanding the biological phenomena. The model successfully reproduces the basic features of morphogenesis in vitro, but mechanism in vivo still remains to be elucidated. (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.

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.