Layers of complexity arise when a person arrives in an Intensive Care Unit (ICU) due to self-harm intended to end their life and when there is known past personal trauma. We highlight three importa...

We argue that while digital health technologies (e.g. artificial intelligence, smartphones, and virtual reality) present significant opportunities for improving the delivery of healthcare, key concepts that are used to evaluate and understand their impact can obscure significant ethical issues related to patient engagement and experience. Specifically, we focus on the concept of empowerment and ask whether it is adequate for addressing some significant ethical concerns that relate to digital health technologies for mental healthcare. We frame these concerns using five key (...) ethical principles for AI ethics (i.e. autonomy, beneficence, non-maleficence, justice, and explicability), which have their roots in the bioethical literature, in order to critically evaluate the role that digital health technologies will have in the future of digital healthcare. (shrink)

We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,ℵ₀)-homogeneous models have multiplicity (Morley degree) 1.

In this paper we study the algebraic structure ofω-stable bilinear maps, arbitrary rings, and nilpotent groups. We will also provide rather complete structure theorems for the above structures in the finite Morley rank case.

Starting from the definition of `amorphous set' in set theory without the axiom of choice, we propose a notion of rank (which will only make sense for, at most, the class of Dedekind finite sets), which is intended to be an analogue in this situation of Morley rank in model theory.

After reviewing the foundations of special relativity and the room left for rival theories, a set of nonrelativistic para-Lorentzian transformations is derived uniquely, based on (a) a weaker first principle, (b) the requirement that the transformations sought do not give rise to the clock “paradox” (in a refined version), and (c) the compliance of the transformations with the classical experiments of Michelson-Morley, Kennedy-Thorndike, and Ives-Stilwell. The corresponding dynamics is developed. Most of the experimental support of special relativity is reconsidered (...) in the light of the new theory. It is concluded that the relativity of simultaneity has so far not been tested. (shrink)

The Fitzgerald-Lorentz contraction hypothesis, proposed as an explanation of the Michelson-Morley result, fails to account for the Kennedy-Thorndike result. Hence, Grünbaum argues, the hypothesis has been falsified. However, the contraction hypothesis as formulated by Lorentz is false for the very fundamental reason that it entails a contradiction, namely, the consequence that light waves must have a variable velocity along what by definition is taken to be a rest length. Furthermore, the attempt to resolve this contradiction by coupling the Fitzgerald-Lorentz (...) contraction with the hypothesis that clock rates are a function of velocity, is open to a sound, methodological objection. The Michelson-Morley result is fully satisfied, provided only that the lengths of the interferometer arms, in the longitudinal and transverse positions, are thought to be related to one another in a certain ratio, and this ratio may be interpreted as a contraction in both arms. Since this twofold contraction hypothesis suffices to explain both the Michelson-Morley and the Kennedy-Thorndike results, and since it entails no contradiction, there is no need to correct both the length of rods and the rate of clocks. Therefore, the combined clock-rod hypothesis, and with it the Fitzgerald-Lorentz contraction hypothesis, must be rejected. (shrink)

The kinematic aspects of the rocket-borne clock experiment by Vessot and Levine are analyzed with the revised Robertson's test theory of special relativity (Found. Phys. 14, 625 (1984)). Besides the expected time-dilation, it is found that the intermediate steps of this experiment yield in principle Michelson-Morley type information (a relation between longitudinal and transverse length contractions) in the third order of the velocities involved, but no relativity-of-simultaneity related effects.The flat space-time test theory induces a family of “spherically symmetric” line (...) elements that become the Schwarzschild line element in the relativistic case and also in theabinito rest frame of the theory. These line elements represent the same space-time manifold, but pertain in a one-to-one correspondence to the different flat space-time coordinate transformations of the test theory. The conserved energy is related to the family of local energies in the tangent plane. No deviations from the orthodoxy appear at the pertinent levels of approximation. Hence the unexplained residuals of the Vessot-Levine experiment are not due in obvious ways to kinematic and gravitational frequency shifts caused by deviations of the “real” coordinate transformations from the Lorentz transformations. (shrink)

The only test theory used by workers in the field of testing special relativity to analyze the significance of their experiments is the proof by H. P. Robertson [Rev. Mod. Phys. 21, 378 (1949)] of the Lorentz transformations from the results of the experimental evidence. Some researchers would argue that the proof contains an unwarranted assumption disguised as a convention about synchronization procedures. Others would say that alternative conventions are possible. In the present paper, no convention is used, but the (...) Lorentz transformations are still obtained using only the results of the experiments in Robertson's proof, namely the Michelson-Morley, Kennedy-Thorndike, and Ives-Stilwell experiments. Thus the revised proof is a valid test theory which is independent of any conventions, since one appeals only to the experimental evidence. The analysis of that evidence shows the directions in which efforts to test special relativity should go. Finally it is shown how the resulting test theory still has to be improved for consistency in the analysis of experiments with complicated experimental setups, how it can be simplified for expediency as to what should be tested, and how it should be completed for a missing step not considered by Robertson. (shrink)

RésuméLe raisonnement selon lequel la simultanéité est relative du point de vue de l'observateur est fondamental dans la Relativité restreinte. Pourtant, l'analyse de ce raisonnement mène aux critiques suivantes:1. Le raisonnement appartient à la physique classique plutǒt qu'à la physique relativiste, en ce qu'il adopte la conception classique de la propagation de la lumière et ignore le principe de la constance de la vitesse de la lumière.2. Il entre en conflit avec l'évidence empirique, car son hypothèse de base et son (...) mode de raisonnement sont presque exactement analogues à ceux qui amenèrent Michelson et Morlay à attendre un résultat positif lors de leur expérience d'interférence.3. Il est logiquement inacceptable, car il repose à la fois sur l'affirmation et sur la négation d'un système de référence privilégié.Bien plus, on montre que l'application correcte des transformations de Lorentz mène non pas à la conclusion que la simultanéité est relative, mais plutǒt à celle qu'elle est absolue.The argument that simultaneity is relative to the viewpoint of an observer, is fundamental to Special Relativity. However, analysis of this argument leads to the following strictures: the argument belongs to classical physics rather than to relativity physics, in that it adheres to the classical view of the propagation of light, and ignores altogether the relativistic principle of the constancy of the velocity of light; the argument conflicts with empirical evidence, in that its basic assumption and mode of reasoning are almost exactly analogous to those which led Michelson and Morley to expect a positive result from their interferometer experiment; the argument is logically untenable, in that it rests on both the affirmation, and the denial, of a privileged frame of reference. Furthermore, it is shown that proper application of the Lorentz transformation, in actually transforming data from one system to another, must lead, not to the conclusion that simultaneity is relative, but rather to the conclusion that it is absolute. (shrink)

Dividing chains have been used as conditions to isolate adequate subclasses of simple theories. In the first part of this paper we present an introduction to the area. We give an overview on fundamental notions and present proofs of some of the basic and well-known facts related to dividing chains in simple theories. In the second part we discuss various characterizations of the subclass of low theories. Our main theorem generalizes and slightly extends a well-known fact about the connection between (...) dividing chains and Morley sequences (in our case: independent sequences). Moreover, we are able to give a proof that is shorter than the original one. This result motivates us to introduce a special property of formulas concerning independent dividing chains: For any dividing chain there exists an independent dividing chain of the same length. We study this property in the context of low, short and ω -categorical simple theories, outline some examples and define subclasses of low and short theories, which imply this property. The results give rise to further studies of the relationships between some subclasses of simple theories. (shrink)

We prove the following theorem. Let G be a connected simple bad group (i.e. of finite Morley rank, nonsolvable and with all the Borel subgroups nilpotent) of minimal Morley rank. Then the Borel subgroups of G are conjugate to each other, and if B is a Borel subgroup of G, then $G = \bigcup_{g \in G}B^g,N_G(B) = B$ , and G has no involutions.

We deal with two forms of the "uniqueness cases" in the classification of large simple K*-groups of finite Morley rank of odd type, where large means the 2-rank m2 is at least three. This substantially extends results known for even larger groups having Prüfer 2-rank at least three, so as to cover the two groups PSp 4 and G 2. With an eye towards more distant developments, we carry out this analysis for L*-groups, a context which is substantially broader (...) than the K* setting. (shrink)

Let G be a simple group of finite Morley rank with a definable BN-pair of rank 2 where B=UT for T=B ∩ N and U a normal subgroup of B with Z≠1. By [9] 853) the Weyl group W=N/T has cardinality 2n with n=3,4,6,8 or 12. We prove here:Theorem 1. If n=3, then G is interpretably isomorphic to PSL3 for some algebraically closed field K.Theorem 2. Suppose Z contains some B-minimal subgroup AZ with RMRM for both parabolic subgroups P1 (...) and P2. Then n=3,4 or 6 and G is interpretably isomorphic to PSL3, PSp4 or G2 for some algebraically closed field K.Theorem 3. If U is nilpotent and n≠8, then G is interpretably isomorphic to either PSL3, PSp4 or G2 for some algebraically closed field K. (shrink)

We define a characteristic and definable subgroup F*(G) of any group G of finite Morley rank that behaves very much like the generalized Fitting subgroup of a finite group. We also prove that semisimple subnormal subgroups of G are all definable and that there are finitely many of them.

We consider a universe of finite Morley rank and the following definable objects: a field math formula, a non-trivial action of a group math formula on a connected abelian group V, and a torus T of G such that math formula. We prove that every T-minimal subgroup of V has Morley rank math formula. Moreover V is a direct sum of math formula-minimal subgroups of the form math formula, where W is T-minimal and ζ is an element of (...) G of order 4 inverting T. (shrink)

The Alperin-Goldschmidt Fusion Theorem [1, 5], when combined with pushing up [7], was a useful tool in the classification of the finite simple groups. Similar theorems are needed in the study of simple groups of finite Morley rank, in the even type case (that is, when the Sylow 2-subgroups are of bounded exponent, as in algebraic groups over fields of characteristic 2). In that context a body of results relating to fusion of 2-elements and the structure of 2-local subgroups (...) is needed: pushing up, and the classification of groups with strongly or weakly embedded subgroups, or have strongly closed abelian subgroups (c.f, [2]). Two theorems of Alperin-Goldschmidt type are proved here. Both are needed in applications.The following is an exact analog of the Alperin-Goldschmidt Fusion Theorem for groups of finite Morley rank, in the case of 2-elements:Theorem 1.1.Let G be a group of finite Morley rank, and P a Sylow2-subgroup of G.If A, B⊆P are conjugate in G, then there are subgroups Hi≤Pand elementsxi∈N(Hi)for1 ≤i≤n,and an elementy∈N(P),such that for all i:1.Hiis a tame intersection of two Sylow2-subgroups;2.CP(Hi) ≤Hi;3.N(Hi)/Hiis2-isolatedand(a)(b). (shrink)

The Schur-Zassenhaus Theorem is one of the fundamental theorems of finite group theory. Here is its statement:Fact1.1 (Schur-Zassenhaus Theorem). Let G be a finite group and let N be a normal subgroup of G. Assume that the order ∣N∣ is relatively prime to the index [G:N]. Then N has a complement in G and any two complements of N are conjugate in G.The proof can be found in most standard books in group theory, e.g., in [S, Chapter 2, Theorem 8.10]. (...) The original statement stipulated one ofNorG/Nto be solvable. Since then, the Feit-Thompson theorem [FT] has been proved and it forces eitherNorG/Nto be solvable. (The analogous Feit-Thompson theorem for groups of finite Morley rank is a long standing open problem).The literal translation of the Schur-Zassenhaus theorem to the finite Morley rank context would state that in a groupGof finite Morley rank a normal π-Hall subgroup (if it exists at all) has a complement and all the complements are conjugate to each other. (Recall that a groupHis called aπ-group, where π is a set of prime numbers, if elements ofHhave finite orders whose prime divisors are from π. Maximal π-subgroups of a groupGare called π-Hall subgroups. They exist by Zorn's lemma. Since a normal π-subgroup ofGis in all the π-Hall subgroups, if a group has a normal π-Hall subgroup then this subgroup is unique.)The second assertion of the Schur-Zassenhaus theorem about the conjugacy of complements is false in general. As a counterexample, consider the multiplicative group ℂ* of the complex number field ℂ and consider thep-Sylow for any primep, or even the torsion part of ℂ*. LetHbe this subgroup.Hhas a complement, but this complement is found by Zorn's Lemma (consider a maximal subgroup that intersectsHtrivially) and the use of Zorn's Lemma is essential. In fact, by Zorn's Lemma, any subgroup that has a trivial intersection withHcan be extended to a complement ofH. Since ℂ* is abelian, these complements cannot be conjugated to each other. (shrink)

We show that if G is a group of finite Morley rank, then the verbal subgroup is of finite width, where w is a concise word. As a byproduct, we show that if G is any abelian-by-finite group, then Gn= is definable.

One of the purposes of this paper is to prove a partial Schur-Zassenhaus Theorem for groups of finite Morley rank.Theorem 2.Let G be a solvable group of finite Morley rank. Let π be a set of primes, and let H ⊲ G a normal π-Hall subgroup. Then H has a complement in G.This result has been proved in [1] with the additional assumption thatGis connected, and thought to be generalized in [2] by the authors of the present article. (...) Unfortunately in the last section of the latter paper there is an irrepairable mistake. Here we give a new proof of the Schur-Zassenhaus Theorem using the results of [2] up to the last section and a new result that we are going to state below.The second author has shown in [11] that a nilpotentω-stable group is the central product of a divisible subgroup and a subgroup of bounded exponent, generalizing a well-known result of Angus Macintyre about abelian groups [8]. One could ask a similar question for solvable groups: are they a product of two subgroups, one divisible, one of bounded exponent? One is allowed to be hopeful because of the well-known decomposition of the connected solvable algebraic groups over algebraically closed fields as the product of the unipotent radical and a torus. (shrink)

We study groups definable in tame expansions of ω-stable theories. Assuming several tameness conditions, we obtain structural theorems for groups definable and interpretable in these expansions. As our main example, by characterizing independence in the pair, where K is an algebraically closed field and G is a multiplicative subgroup of K× with the Mann property, we show that the pair satisfies the assumptions. In particular, this provides a characterization of definable and interpretable groups in in terms of algebraic groups in (...) K and interpretable groups in G. Furthermore, we compute the Morley rank and the U-rank in and both ranks agree. (shrink)

One of the things I attempted to do in my paper on independent testability was to illustrate convincingly the very real difficulties of distinguishing between the accidental and essential features of a scientific experiment. The importance of this distinction is that independent testability presumably requires differences that are essential and telling and not merely accidental reflections of existing experimental technique or of the procedural preferences of the experimenter. In the case of the Michelson-Morley and Kennedy-Thorndike experiments, I showed, following (...) a suggestion of M. G. Evans, that Grünbaum's attempt to distinguish these two experiments does not work. I also showed that certain obvious and natural variations of Grünbaum's approach do not adequately distinguish these experiments. So, for example, it will not do simply to claim that MM is characterized by equal arms and KT by unequal arms, since equal arms are required for MM only in the absence of adequate photographic registration methods. But if these methods are not available then KT is not possible. Conversely, if these methods are available, then while both MM and KT are experimentally possible, MM need not be restricted to equal arms. (shrink)

In this paper the following theorem is proved regarding groups of finite Morley rank which are perfect central extensions of quasisimple algebraic groups.Theorem1.Let G be a perfect group of finite Morley rank and let C0be a definable central subgroup of G such that G/C0is a universal linear algebraic group over an algebraically closed field; that is G is a perfect central extension of finite Morley rank of a universal linear algebraic group. Then C0= 1.Contrary to an impression (...) which exists in some circles, the center of the universal extension of a simple algebraic group, as an abstract group, is not finite in general. Thus the finite Morley rank assumption cannot be omitted.Corollary1.Let G be a perfect group of finite Morley rank such that G/Z(G) is a quasisimple algebraic group. Then G is an algebraic group. In particular, Z(G) is finite([4],Section27.5).An understanding of central extensions of quasisimple linear algebraic groups which are groups of finite Morley rank is necessary for the classification oftamesimpleK*-groupsof finite Morley rank, which constitutes an approach to the Cherlin-Zil’ber conjecture. For this reason the theorem above and its corollary were proven in [1] (Theorems 4.1 and 4.2) under the assumption oftameness, which simplifies the argument considerably. The result of the present paper shows that this assumption can be dropped. The main line of argument is parallel to that in [1]; the absence of the tameness assumption will be countered by a model-theoretic result and results fromK-theory. The model-theoretic result places limitations on definability in stable fields, and may possibly be relevant to eliminating certain other uses of tameness. (shrink)

Let T be superstable. We say a type p is weakly minimal if R(p, L, ∞) = 1. Let $M \models T$ be uncountable and saturated, H = p(M). We say $D \subset H$ is locally modular if for all $X, Y \subset D$ with $X = \operatorname{acl}(X) \cap D, Y = \operatorname{acl}(Y) \cap D$ and $X \cap Y \neq \varnothing$ , dim(X ∪ Y) + dim(X ∩ Y) = dim(X) + dim(Y). Theorem 1. Let p ∈ S(A) be weakly (...) minimal and D the realizations of $\operatorname{stp}(a/A)$ for some a realizing p. Then D is locally modular or p has Morley rank 1. Theorem 2. Let H, G be definable over some finite A, weakly minimal, locally modular and nonorthogonal. Then for all $a \in H\backslash\operatorname{acl}(A), b \in G\operatorname{acl}(A)$ there are a' ∈ H, b' ∈ G such that $a' \in \operatorname{acl}(abb' A)\backslash\operatorname{acl}(aA)$ . Similarly when H and G are the realizations of complete types or strong types over A. (shrink)

Contents: Recursive Enumerability and the Jump Operator; On the Degrees Less Than 0'; A Simple Set Which Is Not Effectively Simple; The Recursively Enumerable Degrees Are Dense; Metarecursive Sets (with G Kreisel); Post's Problem, Admissible Ordinals and Regularity; On a Theorem of Lachlan and Marlin; A Minimal Hyperdegree (with R O Gandy); Measure-Theoretic Uniformity in Recursion Theory and Set Theory; Forcing with Perfect Closed Sets; Recursion in Objects of Finite Type; The a-Finite Injury Method (with S G Simpson); Remarks Against (...) Foundational Activity; Countable Admissible Ordinals and Hyperdegrees; The 1-Section of a Type n Object; The k-Section of a Type n Object; Post's Problem, Absoluteness and Recursion in Finite Types; Effective Bounds on Morley Rank; On the Number of Countable Models; Post's Problem in E-Recursion; The Limits of E-Recursive Enumerability; Effective Versus Proper Forcing. (shrink)

This paper discusses the controversy between philosophers of science (e.g. Grünbaum) and historians of science (e.g. Holton) regarding Einstein's discovery of STR. Although Holton is surely correct on the historical point that experimental results (especially the Michelson-Morley experiment) had little influence on Einstein's development of STR, this fact is not sufficient to establish his (and Polanyi's) claim that major scientific discoveries are primarily matters of private, nonspecifiable insights into physical reality. It is possible that Einstein's work was based primarily (...) on non-empirical but nonetheless publicly discussable, objective considerations. And a more comprehensive survey of the discovery of STR shows that this was indeed the case and thus excludes STR as a supporting instance of Holton's and Polanyi's assertions of the primacy of "private science.". (shrink)

Preferenslogik, av S. Kanger.--Några synpunkter på olika innehållsrelationer, av T. Pauli.--The number of modalities in the Brouwer system supplemented by the axiom schema CL[superscript n]aL[superscript n+1]a, by K. Segerberg.--Konjunktion av ting, av A. H. D. MacLeod.--Über den "Kettensatz der Verpflichtung;" ein Kommentar zu einem Satz der deontischen Logik, von M. Moritz.--Was the ether hypothesis refuted by the Michelson-Morley experiment? By H. Törnebohm.--Die ewige Wiederkunft; ett filosofihistoriskt tidsfördriv, av A. Wedberg.--Some observations on modal logic and philosophical systems, by G. H. (...) von Wright.--Några kommentarer till två varseblivningsteorier, av L. Åquist. (shrink)