We prove that any 1-closed (see def 1.1) model of the Π 2 consequences of PA satisfies ¬Cons PA which gives a proof of the second Godel incompleteness theorem without the use of the Godel diagonal lemma. We prove a few other theorems by the same method.

The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory T in which all partially recursive functions are representable, yet T does not interpret Robinson’s theory R. To this end, we borrow tools from model theory — specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of ∃∀ theories interpretable in (...) existential theories in the process. (shrink)

In this paper we extend of the notion of algebraically closed given in the case of groups and skew fields to an arbitrary h-inductive theory. The main subject of this paper is the study of the notion of positive algebraic closedness and its relationship with the notion of positive closedness and the amalgamation property.

PARC is an "appended numeral" system of natural deduction that I learned as an undergraduate and have taught for many years. Despite its considerable pedagogical strengths, PARC appears to have never been published. The system features explicit "tracking" of premises and assumptions throughout a derivation, the collapsing of indirect proofs into conditional proofs, and a very simple set of quantificational rules without the long list of exceptions that bedevil students learning existential instantiation and universal generalization. The system can be used (...) with any Copi-style set of inference rules, so it is quite adaptable to many mainstream symbolic logic textbooks. Consequently, PARC may be especially attractive to logic teachers who find Jaskowski/Gentzen-style introduction/elimination rules to be far less "natural" than Copi-style rules. The PARC system is also keyboard-friendly in comparison to the widely adopted Jaskowski-style graphical subproof system of natural deduction, viz., Fitch diagrams and Copi "bent arrow" diagrams. (shrink)

Background In June 2016, Canada legalized medical assistance in dying (MAiD). From the outset, some healthcare institutions (including faith-based and non-faith-based hospitals, hospices, and residential aged care facilities) have refused to allow aspects of MAiD onsite, resulting in patient transfers for MAiD assessments and provision. There have been media reports highlighting the negative consequences of these “institutional objections”, however, very little research has examined their nature and impact. Methods This study reports on findings from 48 semi-structured qualitative interviews conducted with (...) MAiD assessors and providers, MAiD team members (working to coordinate care and lead MAiD programs in institutions and health authorities), and family caregivers on their experiences with institutional objection. Participants were recruited from the Canadian provinces of British Columbia, Ontario, and Nova Scotia. Data were analyzed using inductive thematic analysis. Results Themes identified were: (1) basis for institutional objection (with objections commonly rooted in religious values and a particular philosophy of palliative care); (2) scope of objection (demonstrating a wide range of practices objected to); (3) lack of transparency regarding institutional position; (4) impacts on patients; (5) impacts on health practitioners; and (6) catalysts for change. Participants reported that many institutions’ objections had softened over time, lessening barriers to MAiD access and adverse impacts on patients and health practitioners. Participants attributed this positive change to a range of catalysts including advocacy by health practitioners and family members, policymaking by local health authorities, education, and relationship building. Nevertheless, some institutions, particularly faith-based ones, retained strong objections to MAiD, resulting in forced transfers and negative emotional and psychological impacts on patients, family members, and health practitioners. Conclusions This paper adds to the limited evidence base about the impacts of institutional objection and can inform practical and regulatory solutions in Canada and abroad. Reform is needed to minimize the negative impacts on patients, their caregivers, and health practitioners involved in MAiD practice. (shrink)

We study model theory of actions of finite groups on substructures of a stable structure. We give an abstract description of existentially closed actions as above in terms of invariants and PAC structures. We show that if the corresponding PAC property is first order, then the theory of such actions has a model companion. Then, we analyze some particular theories of interest (mostly various theories of fields of positive characteristic) and show that in all the cases considered (...) the PAC property is first order. (shrink)

A total of 1918 loci, detected by the hybridization of 938 expressed sequence tag unigenes from 26 Triticeae cDNA libraries, were mapped to wheat homoeologous group 4 chromosomes using a set of deletion, ditelosomic, and nulli-tetrasomic lines. The 1918 EST loci were not distributed uniformly among the three group 4 chromosomes; 41, 28, and 31% mapped to chromosomes 4A, 4B, and 4D, respectively. This pattern is in contrast to the cumulative results of EST mapping in all homoeologous groups, as reported (...) elsewhere, that found the highest proportion of loci mapped to the B genome. Sixty-five percent of these 1918 loci mapped to the long arms of homoeologous group 4 chromosomes, while 35% mapped to the short arms. The distal regions of chromosome arms showed higher numbers of loci than the proximal regions, with the exception of 4DL. This study confirmed the complex structure of chromosome 4A that contains two reciprocal translocations and two inversions, previously identified. An additional inversion in the centromeric region of 4A was revealed. A consensus map for homoeologous group 4 was developed from 119 ESTs unique to group 4. Forty-nine percent of these ESTs were found to be homoologous to sequences on rice chromosome 3, 12% had matches with sequences on other rice chromosomes, and 39% had no matches with rice sequences at all. Limited homology was found between wheat ESTs on homoeologous group 4 and the Arabidopsis genome. Forty-two percent of the homoeologous group 4 ESTs could be classified into functional categories on the basis of blastX searches against all protein databases. (shrink)

Background Voluntary assisted dying became lawful in Victoria, the first Australian state to permit this practice, in 2019 via the Voluntary Assisted Dying Act 2017 (Vic). While conscientious objection by individual health professionals is protected by the Victorian legislation, objections by institutions are governed by policy. No research has been conducted in Victoria, and very little research conducted internationally, on how institutional objection is experienced by patients seeking assisted dying. Methods 28 semi-structured interviews were conducted with 32 family caregivers and (...) one patient about the experience of 28 patients who sought assisted dying. Participants were interviewed during August-November 2021. Data from the 17 interviews (all with family caregivers) which reported institutional objection were analysed thematically. Results Participants reported institutional objection affecting eligibility assessments, medication access, and taking the medication or having it administered. Institutional objection occurred across health settings and was sometimes communicated obliquely. These objections resulted in delays, transfers, and choices between progressing an assisted dying application and receiving palliative or other care. Participants also reported objections causing adverse emotional experiences and distrust of objecting institutions. Six mediating influences on institutional objections were identified: staff views within objecting institutions; support of external medical practitioners and pharmacists providing assisted dying services; nature of a patient’s illness; progression or state of a patient’s illness; patient’s geographical location; and the capability and assertiveness of a patient and/or caregiver. Conclusions Institutional objection to assisted dying is much-debated yet empirically understudied. This research found that in Victoria, objections were regularly reported by participants and adversely affected access to assisted dying and the wider end-of-life experience for patients and caregivers. This barrier arises in an assisted dying system that is already procedurally challenging, particularly given the limited window patients have to apply. Better regulation may be needed as Victoria’s existing policy approach appears to preference institutional positions over patient’s choice given existing power dynamics. (shrink)

Thematically organized around the major concerns of Basil Bernstein's work as a sociologist, this book includes chapters from some of the leading sociologists and educational scholars. Each section attempts to provide a critical evaluation of Bernstein's work, framed within four interrelated contexts: his sociological theory, sociology of language and code theory, sociology of education and social reproduction, and the influence of his sociology on educational research. In a separate section, Bernstein himself responds to the earlier chapters. The book examines Bernstein's (...) sociology of schools in relation to his general sociological theory and in doing so demonstrates that sociology is an essential lens for understanding the structure and processes of schooling. It also provides a critical evaluation of the strengths and weaknesses of Bernstein's work, as well as a correction to current work in education, which eschews theory in favor of practicality. (shrink)

Paper presented at the Heidegger Circle 2011. Although Aristotle’s influence on young Heidegger’s thought has been studied at length, such studies have almost exclusively focused on his interpretation of Aristotle’s ethics, physics and metaphysics. I will rather address Heidegger’s appropriation of Aristotle’s ontology of life. Focusing on recently published or recently translated courses of the mid 20’s (mainly SS 1924, WS 1925-26 and SS 1926), I hope to uncover an important aspect of young Heidegger’s thought left unconsidered: namely, that Dasein’s (...) existential structures – Befindlichkeit, Understanding and being-with-one-another through language – arose from his close reading of Aristotle’s ontology of life, of animal life. (shrink)

A study of smooth classes whose generic structures have simple theory is carried out in a spirit similar to Hrushovski 147; Simplicity and the Lascar group, preprint, 1997) and Baldwin–Shi 1). We attach to a smooth class K0, of finite -structures a canonical inductive theory TNat, in an extension-by-definition of the language . Here TNat and the class of existentially closed models of =T+,EX, play an important role in description of the theory of the K0,-generic. We show that (...) if M is the K0,-generic then MEX. Furthermore, if this class is an elementary class then Th=Th). The investigations by Hrushovski and Pillay , provide a general theory for forking and simplicity for the nonelementary classes, and using these ideas, we show that if K0,, where {,*}, has the joint embedding property and is closed under the Independence Theorem Diagram then EX is simple. Moreover, we study cases where EX is an elementary class. We introduce the notion of semigenericity and show that if a K0,-semigeneric structure exists then EX is an elementary class and therefore the -theory of K0,-generic is near model complete. By this result we are able to give a new proof for a theorem of Baldwin and Shelah 1359). We conclude this paper by giving an example of a generic structure whose first-order theory is simple. (shrink)

We compare two different notions of generic expansions of countable saturated structures. One kind of genericity is related to existential closure, and another is defined via topological properties and Baire category theory. The second type of genericity was first formulated by Truss for automorphisms. We work with a later generalization, due to Ivanov, to finite tuples of predicates and functions. Let $N$ be a countable saturated model of some complete theory $T$ , and let $(N,\sigma)$ denote an expansion of $N$ (...) to the signature $L_{0}$ which is a model of some universal theory $T_{0}$ . We prove that when all existentially closed models of $T_{0}$ have the same existential theory, $(N,\sigma)$ is Truss generic if and only if $(N,\sigma)$ is an e-atomic model. When $T$ is $\omega$ -categorical and $T_{0}$ has a model companion $T_{\mathrm {mc}}$ , the e-atomic models are simply the atomic models of $T_{\mathrm {mc}}$. (shrink)

We describe classes of existentially closed ordered difference fields and rings. We show an Ax-Kochen type result for a class of valued ordered difference fields.

An Ax-Kochen-Ershov principle for intermediate structures between valued groups and valued fields. We will consider structures that we call valued B-groups and which are of the form $\langle G, B, *, v\rangle$ where - G is an abelian group, - B is an ordered group, - v is a valuation defined on G taking its values in B, - * is an action of B on G satisfying: ∀ x ∈ G ∀ b ∈ B v(x * b) = v(x) (...) · b. The analysis of Kaplanski for valued fields can be adapted to our context and allows us to formulate an Ax-Kochen-Ershov principle for valued B-groups: we axiomatise those which are in some sense existentially closed and also obtain many of their model-theoretical properties. Let us mention some applications: 1. Assume that v(x) = v(nx) for every integer n ≠ 0 and x ∈ G, B is solvable and acts on G in such a way that, for the induced action, $\mathbb{Z}[B] \setminus \{0\}$ embeds in the automorphism group of G. Then $\langle G, B, *, v\rangle$ is decidable if and only if B is decidable as an ordered group. 2. Given a field k and an ordered group B, we consider the generalised power series field k((B)) endowed with its canonical valuation. We consider also the following structure: $\mathbf{M} = \langle k((B))_+, S, v, \times \upharpoonright_{k((B))\times S}\rangle,$ where k((B)) + is the additive group of k((B)), S is a unary predicate interpreting ${T^b| b \in B}$ , and $\times \upharpoonright_{k((B))\times S}$ is the multiplication restricted to k((B))× S, structure which is a reduct of the valued field k((B)) with its canonical cross section. Then our result implies that if B is solvable and decidable as an ordered group, then M is decidable. 3. A valued B-group has a residual group and our Ax-Kochen-Ershov principle remains valid in the context of expansions of residual group and value group. In particular, by adding a residual order we obtain new examples of solvable ordered groups having a decidable theory. (shrink)

The study of existentially closed closure algebras begins with Lipparini’s 1982 paper. After presenting new nonelementary axioms for algebraically closed and existentially closed closure algebras and showing that these nonelementary classes are different, this paper shows that the classes of finitely generic and infinitely generic closure algebras are closed under finite products and bounded Boolean powers, extends part of Hausdorff’s theory of reducible sets to existentially closed closure algebras, and shows that finitely (...) generic and infinitely generic closure algebras are elementarily inequivalent. Special properties of algebraically closed, existentially closed, finitely generic, and infinitely generic closure algebras are established along the way. (shrink)

We study algebraic and model-theoretic properties of existentially closed fields with an action of a fixed finite group. Such fields turn out to be pseudo-algebraically closed in a rather strong sense. We place this work in a more general context of the model theory of fields with a group scheme action.

The class of all Artinian local rings of length at most l is ∀ 2 -elementary, axiomatised by a finite set of axioms Art l . We show that its existentially closed models are Gorenstein, of length exactly l and their residue fields are algebraically closed, and, conversely, every existentially closed model is of this form. The theory Got l of all Artinian local Gorenstein rings of length l with algebraically closed residue field is (...) model complete and the theory Art l is companionable, with model-companion Got l. (shrink)

According to the structured theory of propositions, if two sentences express the same proposition, then they have the same syntactic structure, with corresponding syntactic constituents expressing the same entities. A number of philosophers have recently focused attention on a powerful argument against this theory, based on a result by Bertrand Russell, which shows that the theory of structured propositions is inconsistent in higher order-logic. This paper explores a response to this argument, which involves restricting the scope of the claim (...) that propositions are structured, so that it does not hold for all propositions whatsoever, but only for those which are expressible using closed sentences of a given formal language. We call this restricted principle Closed Structure, and show that it is consistent in classical higher-order logic. As a schematic principle, the strength of Closed Structure is dependent on the chosen language. For its consistency to be philosophically significant, it also needs to be consistent in every extension of the language which the theorist of structured propositions is apt to accept. But, we go on to show, Closed Structure is in fact inconsistent in a very natural extension of the standard language of higher-order logic, which adds resources for plural talk of propositions. We conclude that this particular strategy of restricting the scope of the claim that propositions are structured is not a compelling response to the argument based on Russell’s result, though we note that for some applications, for instance to propositional attitudes, a restricted thesis in the vicinity may hold some promise. (shrink)

A structure is called weakly oligomorphic if its endomorphism monoid has only finitely many invariant relations of every arity. The goal of this paper is to show that the notions of homomorphism‐homogeneity, and weak oligomorphy are not only completely analogous to the classical notions of homogeneity and oligomorphy, but are actually closely related. We first prove a Fraïssé‐type theorem for homomorphism‐homogeneous relational structures. We then show that the countable models of the theories of countable weakly oligomorphic structures are mutually (...) homomorphism‐equivalent (we call first order theories with this property weakly ω‐categorical). Furthermore we show that every weakly oligomorphic homomorphism‐homogeneous structure contains (up to isomorphism) a unique homogeneous, homomorphism‐homogeneous core, to which it is homomorphism‐equivalent. As a consequence we obtain that every countable weakly oligomorphic structure is homomorphism‐equivalent to a finite or ω‐categorical structure. As a corollary we obtain a characterization of positive existential theories of weakly oligomorphic structures as the positive existential parts of ω‐categorical theories. (shrink)

A Boolean product construction is used to give examples of existentially closed algebras in the universal Horn class ISP generated by a universal classKof finitely subdirectly irreducible algebras such that Γa has the Fraser-Horn property. If ⟦a≠b⟧ ∩ ⟦c≠d⟧ = ∅ is definable inKandKhas a model companion ofK-simple algebras, then it is shown that ISP has a model companion. Conversely, a sufficient condition is given for ISP to have no model companion.

The variety of Brouwerian semilattices is amalgamable and locally finite; hence, by well-known results [19], it has a model completion. In this article, we supply a finite and rather simple axiomatization of the model completion.

Abstract.In this paper we show that the theory of fields together with an integrally closed subring, the theory of formally real fields with a real holomorphy ring and the theory of formally \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $p$\end{document}-adic fields with a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $p$\end{document}-adic holomorphy ring have no model companions in the language of fields augmented by a unary predicate for the corresponding ring.

BackgroundThe COVID-19 pandemic has changed the healthcare landscape drastically. Stricken by sharp surges in morbidity and mortality with resource and manpower shortages confounding their efforts, the medical community has witnessed high rates of burnout and post-traumatic stress amongst themselves. Whilst the prevailing literature has offered glimpses into their professional war, no review thus far has collated the deeply personal reflections of physicians and ascertained how their self-concept, self-esteem and perceived self-worth has altered during this crisis. Without adequate intervention, this may (...) have profound effects on their mental and physical health, personal relationships and professional efficacy.MethodsWith mentions of the coronavirus pervading social media by the millions, this paper set out to collate and thematically analyse social media posts containing first-person physician reflections on how COVID-19 affected their lives and their coping mechanisms. A consistent search strategy was employed and a PRISMA flowchart was used to map out the inclusion/exclusion criteria.ResultsA total of 590 social media posts were screened, 511 evaluated, and 108 included for analysis. Salient themes identified include Disruptions to Personal Psycho-Emotional State, Disruptions to Professional Care Delivery, Concern for Family, Response from Institution, Response from Society and Coping Mechanisms.ConclusionIt is evident that the distress experienced by physicians during this time has been manifold, multi-faceted and dominantly negative. Self-concepts were distorted with weakened self-esteem and perceived self-worth observed. The Ring Theory of Personhood (RToP) was adopted to explain COVID-19’s impact on physician personhood as it considers existential, individual, relational and social concepts of the self. These entwined self-concepts serve as ‘compensatory’ to one another, with coping mechanisms buffering and fortifying the physician’s overall personhood. With healthcare institutions playing a vital role in providing timely and targeted support, it was further proposed that a comprehensive assessment tool based on the RToP could be developed to detect at-risk physicians and evaluate the presence and effectiveness of established support structures. (shrink)

This corrigendum concerns [, § ] on ordered difference existentially closed valued fields where we overlooked the problem of immediate extensions.

The underlying modules of existentially closed ▵-algebras are studied. Among other things, it is proved that they are all elementarily equivalent, and that all of them are existentially closed as modules if and only if ▵ is regular. It is also proved that every saturated module in the appropriate elementary equivalence class underlies an e.c. ▵-algebra. Applications to some problems in module theory are given. A number of open questions are mentioned.

We prove that there are 2 χ 0 pairwise non elementarily equivalent existentially closed ordered groups, which solve the main open problem in this area (cf. [3, 10]). A simple direct proof is given of the weaker fact that the theory of ordered groups has no model companion; the case of the ordered division rings over a field k is also investigated. Our main result uses constructible sets and can be put in an abstract general framework. Comparison with (...) the standard methods which use forcing (cf. [4]) is sketched. (shrink)

We give geometric axioms for existentially closed Hasse fields. We prove a quantifier elimination result for existentially closed n-truncated Hasse fields and characterize them as reducts of existentially closed Hasse fields.

We point out that the theory of difference fields with algebraically closed fixed field has no model companion.

We continue the analysis of foundations of positive model theory as introduced by Ben Yaacov and Poizat. The objects of this analysis are $h$-inductive theories and their models, especially the “positively” existentially closed ones. We analyze topological properties of spaces of types, introduce forms of quantifier elimination, and characterize minimal completions of arbitrary $h$-inductive theories. The main technical tools consist of various forms of amalgamations in special classes of structures.

This article constitutes an attempt to articulate productive crossovers between some of the philosophical groundings and theoretical underpinnings on which various schools of phenomenology are based and areas within the practice and theory of psychoanalysis that chime with these. It works ultimately towards establishing a _phenomenologico-existential psychoanalysis _from these researches, out of which key concepts of illness, structure, situation, and periodicity are excavated; and into which they are incorporated.

For a quasi variety of algebras K, the Higman Theorem is said to be true if every recursively presented K-algebra is embeddable into a finitely presented K-algebra; the Generalized Higman Theorem is said to be true if any K-algebra which is recursively presented over its finitely generated subalgebra is embeddable into a K-algebra which is finitely presented over this subalgebra. We suggest certain general conditions on K under which the Higman Theorem implies the Generalized Higman Theorem; a finitely generated K-algebra (...) A is embeddable into every existentially closed K-algebra containing a finitely generated K-algebra B if and only if the word problem for A is Q-reducible to the word problem for B. The quasi varieties of groups, torsion-free groups, and semigroups satisfy these conditions. (shrink)

Bounded PAC substructures of models of stable theory T are generalizations of bounded PAC fields and bounded PAC beautiful pairs generalize Poizat's beautiful pairs. Both notions were introduced in the authors Ph.D. thesis. In this paper, we prove that under the assumption that the PAC property is first order for T, the theory of any bounded PAC structure is simple. Moreover, if the PAC property is first order for T and T does not have the finite cover property, then (...) the theory of any bounded PAC beautiful pair is simple. We, also, give a characterization of dividing in both cases. (shrink)

We consider existentially closed fields with several orderings, valuations, and [Formula: see text]-valuations. We show that these structures are NTP2 of finite burden, but usually have the independence property. Moreover, forking agrees with dividing, and forking can be characterized in terms of forking in ACVF, RCF, and [Formula: see text]CF.

We consider existentially closed fields with several orderings, valuations, and p-valuations. We show that these structures are NTP2 of finite burden, but usually have the independence property. Mo...

The paper argues that the view that the particular quantifier is ‘existentially loaded’ is a relatively new one historically and that it has become entrenched in modern philosophical logic for less than happy reasons.

The technological virtual converges with our contemporary existence in a multitude of ways, which suggests a need to interrogate the question of the virtual existentially. Merleau-Ponty’s existential phenomenological account of embodiment is invaluable in this regard because the virtual is encountered from the basis of the facticity of the embodied individual – a facticity that is closely related to perception and motor intentionality. The current article argues that these characteristics of the body-subject should be taken into consideration in order (...) to develop a clearer description of the virtual. However, beyond an embodied account that relates to early technologies, Merleau-Ponty also presents through his concept of the flesh a novel avenue for the ontological investigation of the virtual. The flesh describes the intertwining of the body-subject and the world, which is suggestive of a new account of the individual’s sensibility in relation to the virtual. An original concept is suggested to describe the existential-ontological structure of the virtual: The embodied screen. The embodied screen as neologism presents an alternative conceptualisation of the coincidence of the body-subject (who understands the world spatially) with the virtual (as non-spatial). By tracing imaginative signification and embodied habitude in terms of the virtual, this article suggests certain existential implications of the virtual for contemporary being. (shrink)

In this paper I offer an alternative phenomenological account of depression as consisting of a degradation of the degree to which one is situated in and attuned to the world. This account contrasts with recent accounts of depression offered by Matthew Ratcliffe and others. Ratcliffe develops an account in which depression is understood in terms of deep moods, or existential feelings, such as guilt or hopelessness. Such moods are capable of limiting the kinds of significance and meaning that one can (...) come across in the world. I argue that Ratcliffe’s account is unnecessarily constrained, making sense of the experience of depression by appealing only to changes in the mode of human existence. Drawing on Merleau-Ponty’s critique of traditional transcendental phenomenology, I show that many cases of severe psychiatric disorders are best understood as changes in the very structure of human existence, rather than changes in the mode of human existence. Working in this vein, I argue that we can make better sense of many first-person reports of the experience of depression by appealing to a loss or degradation of the degree to which one is situated in and attuned to the world, rather than attempting to make sense of depression as a particular mode of being situated and attuned. Finally, I argue that drawing distinctions between disorders of structure and mode will allow us to improve upon the currently heterogeneous categories of disorder offered in the DSM-5. (shrink)

The least common subsumer of a set of concept descriptions is the most specific concept description that subsumes all of the concept descriptions in the given set. By computing the lcs, commonalities between concept descriptions can be made explicit. This is an important inference task useful in several applications, including, for instance, the bottom-up construction of description logic knowledge bases. Previous work on the lcs has concentrated on description logics that either allow for number restrictions or for existential restrictions. Many (...) applications, however, require to combine these constructors. In this work, we present an algorithm for computing the lcs in the description logic ALEN which comprises both constructors—number and existential restrictions—as well as concept conjunction, primitive negation, and value restrictions. To prove correctness of our lcs algorithm, we develop a structural characterization of subsumption in ALEN. (shrink)