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.

Transvertebral magnetic stimulation (TVMS) of the human lumbar spinal cord can evoke bilateral rhythmic leg movements, as in walking, supposedly through the activation of spinal locomotor neural circuitry. However, an appropriate stimulus intensity that can effectively drive the human spinal locomotor circuitry to evoke walking-like movements has not been determined. To address this issue, TVMS was delivered over an intervertebral space of the lumbar cord (L1–L3) at different stimulus intensities (10–70% of maximum stimulator output) in healthy human adults. In a (...) stimulus intensity-dependent manner, TVMS evoked two major patterns of rhythmic leg movements in which the left-right movement cycles were coordinated with different phase relationships: hopping-like movements, in which both legs moved in the same direction in phase, and walking-like movements, in which both legs moved alternatively in anti-phase; uncategorized movements were also observed which could not be categorized as either movement type. Even at the same stimulation site, the stimulus-evoked rhythmic movements changed from hopping-like movements to walking-like movements as stimulus intensity was increased. Different leg muscle activation patterns were engaged in the induction of the hopping- and walking-like movements. The magnitude of the evoked hopping- and walking-like movements was positively correlated with stimulus intensity. The human spinal neural circuitry required a higher intensity of magnetic stimulation to produce walking-like leg movements than to produce hopping-like movements. These results suggest that TVMS activates distinct neural modules in the human spinal cord to generate hopping- and walking-like movements. (shrink)

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 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.

Many functional glycoproteins are expressed on the lymphocyte cell surface. Some of them carry O-linked oligosaccharides (O-glycans), which are conjugated through serine or threonine residues. During various biological processes, including T-cell activation, a tetrasaccharide on the T-cell surface is dramatically converted to a branched hexasaccharide, called core2 O-glycan. The same structural change in O-glycans is also found on the lymphocytes from patients with immunodeficiency conditions such as Wiskott-Aldrich syndrome and AIDS. Several studies revealing the roles of core2 O-glycans in immune (...) responses show that this is a biologically significant change. In particular, core2 O-glycans expressed on the cell surface reduce cell–cell interactions, thereby regulating immune responses. Furthermore, core2 O-glycan is a key backbone structure in forming selectin ligands. Thus, O-linked oligosaccharides, in particular those containing core2 branches, play vital roles in immune responses and may play dual roles in certain situations. This review will summarize the results obtained from various studies investigating the roles of O-glycans in immunological processes. BioEssays 23:46–53, 2001. © 2001 John Wiley & Sons, Inc. (shrink)

Many functional glycoproteins are expressed on the lymphocyte cell surface. Some of them carry O-linked oligosaccharides (O-glycans), which are conjugated through serine or threonine residues. During various biological processes, including T-cell activation, a tetrasaccharide on the T-cell surface is dramatically converted to a branched hexasaccharide, called core2 O-glycan. The same structural change in O-glycans is also found on the lymphocytes from patients with immunodeficiency conditions such as Wiskott-Aldrich syndrome and AIDS. Several studies revealing the roles of core2 O-glycans in immune (...) responses show that this is a biologically significant change. In particular, core2 O-glycans expressed on the cell surface reduce cell–cell interactions, thereby regulating immune responses. Furthermore, core2 O-glycan is a key backbone structure in forming selectin ligands. Thus, O-linked oligosaccharides, in particular those containing core2 branches, play vital roles in immune responses and may play dual roles in certain situations. This review will summarize the results obtained from various studies investigating the roles of O-glycans in immunological processes. BioEssays 23:46–53, 2001. © 2001 John Wiley & Sons, Inc. (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 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)

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 concept of evolvability—the capacity of a population to produce and maintain evolutionarily relevant variation—has become increasingly prominent in evolutionary biology. Paleontology has a long history of investigating questions of evolvability, but paleontological thinking has tended to neglect recent discussions, because many tools used in the current evolvability literature are challenging to apply to the fossil record. The fundamental difficulty is how to disentangle whether the causes of evolutionary patterns arise from variational properties of traits or lineages rather than being (...) due to selection and ecological success. Despite these obstacles, the fossil record offers unique and growing sources of data that capture evolutionary patterns of sustained duration and significance otherwise inaccessible to evolutionary biologists. Additionally, there exist a variety of strategic possibilities for combining prominent neontological approaches to evolvability with those from paleontology. We illustrate three of these possibilities with quantitative genetics, evolutionary developmental biology, and phylogenetic models of macroevolution. In conclusion, we provide a methodological schema that focuses on the conceptualization, measurement, and testing of hypotheses to motivate and provide guidance for future empirical and theoretical studies of evolvability in the fossil record. (shrink)

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.

IntroductionDeep brain stimulation is an effective treatment for advanced Parkinson’s disease with the targeting bilateral subthalamic nucleus or globus pallidus internus. So far, detailed studies on the efficacy of unilateral STN-DBS for motor symptoms have been reported, but few studies have been conducted on unilateral GPi-DBS.Materials and MethodsSeventeen patients with Parkinson’s disease who underwent unilateral GPi-DBS were selected. We conducted comparison analyses between scores obtained 6–42 months pre- and postoperatively using the following measurement tools: the Movement Disorder Society Unified Parkinson’s (...) Disease Rating Scale part III, the Hoehn and Yahr stage, the presence/absence of dyskinesia, Mini-Mental State Examination, Frontal Assessment Battery, Geriatric Depression Scale, levodopa equivalent dose, and cerebral blood flow by single photon emission computed tomography. Patient backgrounds were compared between four cohorts with favorable and unfavorable postoperative outcome.ResultsSignificant improvement was observed postoperatively in the following: total MDS-UPDRS Part III scores during the off period, contralateral scores, ipsilateral scores, and axial scores. Similarly, the Hoehn and Yahr stages during the off period, and GDS also showed significant decrease. In contrast, LED, MMSE, and FAB remained unchanged while the number of patients who scored positive for dyskinesia decreased by 40%. Abnormal cerebral blood flow preoperatively seen in the cerebral cortex had normalized in the total score-based good responder cohort. In the ipsilateral score-based good responder cohort, cerebral blood flow increased in the contralateral frontal lobe including in the premotor cortex, contralateral to the DBS. Compared to the poor responders, postoperative good responders demonstrated significantly higher preoperative MMSE scores.DiscussionUnilateral GPi-DBS therapy was effective in improving contralateral, ipsilateral, and axial motor symptoms of patients with advanced PD; in particular, it was found to be especially beneficial in PwPD whose cognitive function was unimpaired; the treatment efficacy rivaled that of bilateral counterparts up till at least 6 months postoperatively. Finally, normalization of preoperative abnormalities in cerebral blood flow and increased cerebral blood flow in the contralateral frontal lobe indicated the beneficial potential of this therapy on ipsilateral motor symptoms. (shrink)

Background: Freezing of gait is a common symptom in Parkinson’s disease and can be difficult to treat with dopaminergic medications or with deep brain stimulation. Novel stimulation paradigms have been proposed to address suboptimal responses to conventional DBS programming methods. Burst-cycling deep brain stimulation delivers current in various frequencies of bursts, while maintaining an intra-burst frequency identical to conventional DBS.Objective: To evaluate the safety and tolerability of BCDBS in PD patients with FOG.Methods: Ten PD subjects with STN or GPi DBS (...) and complaints of FOG were recruited for this single center, single blinded within-subject crossover study. For each subject, we compared 4, 10, and 15 Hz BCDBS to conventional DBS during the PD medication-OFF state.Results: There were no serious adverse events with BCDBS. It was feasible and straightforward to program BCDBS in the clinic setting. The benefit was comparable to conventional DBS in measures of FOG, functional mobility and in PD motor symptoms. BCDBS had lower battery consumption when compared to conventional DBS.Conclusions: BCDBS was feasible, safe and well tolerated and it has potential to be a viable future DBS programming strategy. (shrink)

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.

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.