In this note we shall show that if L is a balanced pseudocomplemented Ockham algebra then the set ${\fancyscript{I}_{k}(L)}$ of kernel ideals of L is a Heyting lattice that is isomorphic to the lattice of congruences on B(L) where ${B(L) = \{x^* | x \in L\}}$ . In particular, we show that ${\fancyscript{I}_{k}(L)}$ is boolean if and only if B(L) is finite, if and only if every kernel ideal of L is principal.

In this note, it is shown that the set of kernel ideals of a K n, 0-algebra L is a complete Heyting algebra, and the largest congruence on L such that the given kernel ideal as its congruence class is derived and finally, the necessary and sufficient conditions that such a congruence is pro-boolean are given.

We consider, in the context of an MS-algebra L, the ideals I of L that are kernels of L. We characterize two kinds of de Morgan algebras: the class Boolean algebras and the absolutely indecomposable de Morgan algebras. We show that all the e-ideals I of L are kernel ideals of L if and only if the subalgebra \ of L can only be these two kinds of de Morgan algebras.

We identify the \-ideals of a distributive demi-pseudocomplemented algebra L as the kernels of the boolean congruences on L, and show that they form a complete Heyting algebra which is isomorphic to the interval \ of the congruence lattice of L where G is the Glivenko congruence. We also show that the notions of maximal \-ideal, prime \-ideal, and falsity ideal coincide.

Book synopsis: In this combative major new work, philosophical sharpshooter Slavoj Zizek looks for the kernel of truth in the totalitarian politics of the past. Examining Heidegger's seduction by fascism and Foucault's flirtation with the Iranian Revolution, he suggests that these were the 'right steps in the wrong direction.' On the revolutionary terror of Robespierre, Mao and the bolsheviks, Zizek argues that while these struggles ended in historic failure and horror, there was a valuable core of idealism lost beneath (...) the bloodshed. A redemptive vision has been obscured by the soft, decentralized politics of the liberal-democratic consensus. Faced with the coming ecological crisis, Zizekk argues the case for revolutionary terror and the dictatorship of the proletariat. A return to past ideals is needed despite the risks. In the words of Samuel Beckett: 'Try again. Fail again. Fail better.'. (shrink)

N4-lattices provide algebraic semantics for the logic N4, the paraconsistent variant of Nelson's logic with strong negation. We obtain the representation of N4-lattices showing that the structure of an arbitrary N4-lattice is completely determined by a suitable implicative lattice with distinguished filter and ideal. We introduce also special filters on N4-lattices and prove that special filters are exactly kernels of homomorphisms. Criteria of embeddability and to be a homomorphic image are obtained for N4-lattices in terms of the above mentioned (...) representation. Finally, subdirectly irreducible N4-lattices are described. (shrink)

Heart of Darkness is the story of a quest for truth but a quest, we discover, that is veiled in ironies. But just how radical are these ironies? When Marlow tells us that Kurtz’s dying whisper enunciates a truth, does he give us a solid kernel around which we can build our further questioning, concerning, for example, whether Marlow preserves or betrays the truth he has been given?” This has been the assumption of most critics; regardless of the ingenuities (...) by which the varieties of interpretation has shown that Marlow in the end lies or does not lie, the axis of interpretation has almost always been defined by Kurtz’s presumed truth. Why should this be so? Why should Kurtz’s whisper be more significant than, say, the cry of the Intended with which the story culminates? But there are presuppositions in force here so strong that it seems senseless to ask this question. Classic presuppositions: the woman is dominated by emotion and desire, and her cry is at the other pole from the nonlibidinal utterance of truth. Marlow would agree with this assessment—for him, women are “out of touch with the truth” which you have to be “man enough” to face. So our truth-seeking criticism, which doubts much of what Marlow says, does not doubt the terms in which Marlow conceives of truth and its authority.Let us consider an example of the truth-seeking reading of Heart of Darkness, examining the ideology that sanctions this form of interpretation and showing how its presuppositions cooperate with Marlow’s. Our specimen will be a fairly recent PMLA article by Garrett Stewart called “Lying as Dying in Heart of Darkness.” Stewart’s “existential” reading invokes an economics of truth: Kurtz truthfully confronts death, facing and passing judgment upon the corruption of his being that emerges as fulfilled in his final moment; Marlow “lives through” Kurtz’s death and has the opportunity to preserve and transmit Kurtz’s “legacy of insight”; his lie, however, “kills the meaning of a death,” “squandering … Kurtz’s delegated revelation on a squeamish deceit.”1 1. Garrett Stewart, “Lying as Dying in Heart of Darkness,” PMLA 95 : 330, 329, 326; all further references to this essay, abbreviated “L,” will be included in the text. Henry Staten is associate professor of English and adjunct associate professor of philosophy at the University of Utah. He is the author of Wittgenstein and Derrida. The present essay is part of a book in progress on mourning and idealization in Western literature. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:In Search of the ClassicEdward E. FosterIn Search of the Classic, by Steven Shankman; xvi & 331 pp. University Park: Pennsylvania State University Press, 1995, $55.00 cloth, $18.95 paper.“In search of” in the title of a book is often a code warning of lukewarm conviction or academic disingenuousness. In Shankman’s title, however, the phrase is literally appropriate because he forthrightly argues that the classic is, of its nature, (...) something that always exists in quest and tension. The classic is not to be located merely in classical antiquity or in the tastes of a privileged class. Though Shankman grants that these often are associated with the literary classic, he finds the nature of the classic rather in the nature of literature as a state of metaxis or “in-betweenness.” His examinations of classical, neo-classical, and modern works define various aspects of this “in-betweenness,” the state of tension that exists in the truly classic at any point in the history of literature.Although Shankman dismisses Derrida, Foucault, de Man, and others for having mistaken their own destruction of Enlightenment rationalism for a demonstration that rationality is impossible, he is not wildly original. He uses Habermas’s notion of classic literature as enduring and independent of time and Vogelin’s concept of metaxis as foundational for his sprawling, yet lucid, inquiry into the idea of the classic in Homer, Plato, Aristotle, Pindar, Virgil, Dryden, Defoe, Swift, Valery, and others, and in the traditions of the epic, ode, pastoral, and lyric.Fundamental is the view that classic literature has the greatest power to represent human experience. To avoid the hermeneutical conundrum of the subject-object dilemma, Shankman asserts literature to be in “a middle place” from Plato and Aristotle on. He sees a basic agreement between them on how literature stands between the One and the Many. Put negatively, literature is not sparks from the One or compilations of the Many. Rather it is a mediator between these polarities: classic literature accommodates the propositional purity of philosophy to the indeterminacy of thing-reality. Literature is neither an abstract kernelization of truth nor an anthology of the things of experience [End Page 256] but an analogical conjunction of the two extremes—therefore tension, therefore continual quest.Using Plato, especially the Cratylus and the Symposium, and Aristotle, especially the Metaphysics and the Poetics, Shankman describes a rationality that exists in literature that is clearly identified in his chapter on Swift’s Gulliver’s Travels by emphasizing the idea of man as an animal capax rationis. This in itself places man’s literary enterprise in a middle place and Shankman explores its various implications in a variety of works. From this perspective, it is argued that literature must be about something that matters; that pure poetry or reflexive poetry cannot achieve the ambiguity of analogy as the central core that the classic requires. Thus, Plato never rejected poetry—only the debasement of poetry into either the fantastical or literal (or the confusion of the two.)The true classic walks a line between ignorance and knowledge, rhetoric and philosophy, literalism and fantasy, “thing-reality” and “the ideal.” The Aeneid makes a good test case. It is at once a piece of propaganda and a statement of an ideal that is complicated by the duplicity of Aeneas’ abandonment of Dido, the brutality of his killing of Turnus, and his emergence in Book VI from the underworld by the Gate of Ivory (false dreams). Such tension is exemplary of what Shankman sinuously argues is at the heart of “the classic” in a variety of other works.The argument is persuasive and attractive, even if not compelling, in a world where many critics would have us believe that all of literature, canonical or not, is disappearing into nontext. That about half of the chapters are adaptations of previously published articles risks a discontinuity that is largely avoided by recapitulations of where we are in the exposition of our struggle in a continuing and intrinsic state of rational metaxis. I like the idea, but I must reserve judgment on a thesis that attends to the poetry of Yvor Winters and E. V. Cunningham... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Osip Mandelstam and the Modernist Creation of TraditionHarold D. BakerOsip Mandelstam and the Modernist Creation of Tradition, by Clare Cavanagh; xii & 365 pp. Princeton: Princeton University Press, 1995, $39.50.The great, enigmatic poet of twentieth-century Russia, Osip Mandelstam (1891–1938), employed a poetics based on recollection. The word-soul or psyche is not contained within a linguistic body but hovers amorously over it, [End Page 257] fleeing any too crude (...) attempt at capture. The reader must trace out Mandelstam’s personal networks of association, both inside and outside the text, before a kernel of thought and emotion can be recognized (“only the moment of recognition is sweet to us,” goes a famous line from his “Tristia”). Although Clare Cavanagh’s book does not emphasize this theme, her tactics could hardly be better suited to Mandelstam’s peculiar poetic sensibility.Osip Mandelstam and the Modernist Creation of Tradition is an exhaustive exploration of historical and cultural context. It opposes itself explicitly to the traditional structuralist and semiotic approaches to Mandelstam, and takes his works in their “secular” rather than their “hermetic” aspect (to borrow terms from Robert Scholes). In that sense it seeks to recollect and bring to mind everything that might affect our understanding of Mandelstam’s oeuvre. This turns out to be a varied field: Pound and Eliot (coeval modernists whose ideas resonate significantly with his), François Villon, Byzantine and Gothic church architecture, the marginalized yet culturally dynamic position of the Russian Jew, Pindar (an exemplar of the social-economic relation of poet to state), Dante, the psychology of literary play, and even Charlie Chaplin. Although it does not use extensive biographical framing, the book proceeds through Mandelstam’s poetry and prose in chronological order, alternately pursuing aspects of context and concentrating on selected works by Mandelstam for sustained analysis.What results is perhaps the most serious comprehensive work on the poet produced so far. Cavanagh’s approach may appear diffuse at first, but it enables her to capture a great deal of this elusive genius without confining Mandelstam within a narrow critical purview. The book’s argument is that Mandelstam qualifies as a central modernist poet through his agonistic relation to an ideal of “world culture.” He attempts to recreate an authoritative literary and cultural tradition that his own innovative work would both continue and transform. And it is from this point of view that Mandelstam’s Jewishness appears so significant to Cavanagh (a chief issue in three out of eight chapters): it gives a precise formula for that position both inside and outside of the dominant culture. Cavanagh even contends quite suggestively that, for Mandelstam, both Dante and Chaplin function as avatars of Jewishness.All this is well-founded and important, but perhaps the best thing about her book is that its central argument doesn’t do justice to the richness of Cavanagh’s own materials. Her discussion does not weaken, for instance, as it leaves Mandelstam’s early period, when the notion of “world culture” was indeed an obsessive one for him. The book is equally effective on the brilliant late poems of the Voronezh cycle, by which time not only a place in world culture but even a secure place in human society seemed futile dreams to Mandelstam. Cavanagh’s readings of the prose and especially the poetry are flexible and sensitive; she gives beautiful accounts of the poetic wordplay and follows closely the ebb and flow of musicality in the verse from one period and [End Page 258] collection to another. More than a milestone in Mandelstam studies, this book brings the poet closer to realizing his fondest dream: a responsive, understanding readership or “interlocutor.”Harold D. BakerUniversity of California, IrvineCopyright © 1996 The Johns Hopkins University Press... (shrink)

This is the second volume of an "essay in existential philosophy." The first, published in 1977, was intended to "do justice to certain experiential givens of immediate experience" which, once subjected to "severe" testing, could be established as "scientific hypotheses at the level of an existential critique of knowledge". The second volume now means to provide "an ensemble of ideal base intuitions, expressible as a 'system', of which each constitutes the concrete taking of a position before a certain state (...) of things in the existential domain". Its method is to work from descriptions of "the existent in the domain of action" in order to find "kernels of convergence, centers of autonomy, that is structures," and so to be able to ask, finally, about the ground of these in a transcendent act of being. (shrink)

The Motoneurone and its Muscle Fibres presents a state-of-the-art summary of knowledge concerning the motoneurones, vital for innervating and commanding skeletal muscles. No muscle action would be possible without motoneurones. These cells are therefore absolutely essential for the execution of normal behaviour and for life support. It is their degeneration that leads to various kinds of motoneurone disease that are often ultimately lethal. However, the study of motoneurones is also important for general insights as to how neurones work, because the (...) motoneurone is probably the best understood kind of nerve cell so far in neuroscience. Motoneurones of the spinal cord were the first type of central nerve cell to be subjected to detailed physiological measurements, and much is known about how their activity is regulated by synapses from other central neurones. For most of the individual neurones within the central nervous system, the precise functional tasks are difficult to define. However, for motoneurones much is now known about their short- and long-term interactions with their main targets, the skeletal muscle fibres. Functions of neurones must be analyzed in relation to the response properties of their target cells. Therefore, this book deals with both, summarizing classical as well as recent knowledge concerning the motoneurone and its muscle fibres. This is the first time that so many aspects of this broad subject matter are treated in one comprehensive monograph. (shrink)

This article discusses the concept of publicity in Kant’s moral philosophy. Insofar as the concepts of ‘public’ and ‘private’ can describe our relations with others, they can be considered to be moral concepts. I argue that we can find in Kant a moral duty not to keep our maxims of action private, or secret. Whereas Korsgaard argues that sometimes in the face of evil it is permissible to sidestep the moral law, I argue that it is rather through publicity that (...) we can deal with evil in the non-ideal world. Moreover, by being open with our maxims, moral progress is possible. View HTML Send article to KindleTo send this article to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle. Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply. Find out more about the Kindle Personal Document Service.Making the Ideal Real: Publicity and Morality in KantVolume 21, Issue 2Melissa Zinkin DOI: https://doi.org/10.1017/S1369415416000042Your Kindle email address Please provide your Kindle [email protected]@kindle.com Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Dropbox To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox. Making the Ideal Real: Publicity and Morality in KantVolume 21, Issue 2Melissa Zinkin DOI: https://doi.org/10.1017/S1369415416000042Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Send article to Google Drive To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive. Making the Ideal Real: Publicity and Morality in KantVolume 21, Issue 2Melissa Zinkin DOI: https://doi.org/10.1017/S1369415416000042Available formats PDF Please select a format to send. By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services. Please confirm that you accept the terms of use. Cancel Send ×Export citation. (shrink)

The Ideal Worlds Account of Desire says that S wants p just in case all of S’s most highly preferred doxastic possibilities make p true. The account predicts that a desire report ⌜S wants p⌝ should be true so long as there is some doxastic p-possibility that is most preferred. But we present a novel argument showing that this prediction is incorrect. More positively, we take our examples to support alternative analyses of desire, and close by briefly considering what (...) our cases suggest about the logic of desire. (shrink)

E.V. Ilyenkov is widely considered to be the most important Soviet philosopher in the post-Stalin period. He is known largely for his original conception of the ideal, which he deployed against both idealist and crude materialist forms of reductionism, including official Soviet Diamat. This conception was articulated in its most developed form in ‘Dialectics of the Ideal’, which was written in the mid-1970s but prevented from publication in its complete form until thirty years after the author’s death. The (...) translation before you provides for the first time the complete, unabridged and unedited text of ‘Dialectics of the Ideal’ in English translation, including the author’s own subsequent comments on the text. (shrink)

While the debate on values in science focuses on normative questions on the level of the individual (e.g. should researchers try to make their work as value free as possible?), comparatively little attention has been paid to the institutional and professional norms that researchers are expected to follow. To address this knowledge gap, we conduct a content analysis of leading national codes of conduct for research integrity of European countries, and structure our analysis around the question: do these documents allow (...) for researchers to be influenced by “non-epistemic” (moral, cultural, commercial, political, etc.) values or do they prohibit such influence in compliance with the value-free ideal (VFI) of science? Our results return a complex picture. On the one hand, codes of conduct consider many non-epistemic values to be a legitimate influence on the decision-making of researchers. On the other, most of these documents include what we call _VFI-like positions_: passages claiming that researchers should be free and independent from any external influence. This shows that while many research integrity documents do not fully endorse the VFI, they do not reject it and continue to be implicitly influenced by it. This results in internal tensions and underdetermined guidance on non-epistemic values that may limit some of the uses of research integrity codes, especially for purposes of ethical self-regulation. While codes of conduct cannot be expected to decide how researchers should act in every instance, we do suggest that they acknowledge the challenges of how to integrate non-epistemic values in research in a more explicit fashion. (shrink)

What are the appropriate criteria for assessing a theory of morality? In this enlightening work, Brad Hooker begins by answering this question. He then argues for a rule-consequentialist theory which, in part, asserts that acts should be assessed morally in terms of impartially justified rules. In the end, he considers the implications of rule-consequentialism for several current controversies in practical ethics, making this clearly written, engaging book the best overall statement of this approach to ethics.

SUPPORTERS of a coherentist standard of truth must be able to establish that this criterion is duly consonant with the definitional nature of truth, for there ought rightfully to be a continuity between our evidential criterion of acceptability-as-true and the "truth" as definitionally specified. Any satisfactory criterion must be such as to yield the real thing--at any rate in sufficiently favorable circumstances. Fortunately for coherentism, it is possible to demonstrate rigorously that truth is tantamount to ideal coherence--that a proposition's (...) being true is in fact equivalent with its being optimally coherent with an ideal data base. Given that the preceding continuity requirement is satisfied, the traditional view of truth as accord with fact is thus also available to coherentists. However, the element of idealization at issue means that we cannot claim that coherence provides us with unqualified truth in actual practice. The coherence-based inquiries we actually carry out, can go only so far as to afford our best available estimate of the real truth. (shrink)

How should we pursue aesthetic value, or incorporate it into our lives, if we want to? Is there an ideal of aesthetic life? Philosophers have proposed numerous answers to the analogous question in moral philosophy, but the aesthetic question has received relatively little attention. There is, in essence, a single view, which is that one should develop a sensibility that would give one sweeping access to aesthetic value. I challenge this view on two grounds. First, it threatens to undermine (...) our "aesthetic love", or the meaningful attachments we form with aesthetic items, e.g., poems, paintings, songs, or items of design and dress. Second, it fails to accommodate the motivational character of our encounter with beauty, which can diminish our desire to pursue the wider world of aesthetic value. I conclude that whatever the aesthetic ideal is, it must reconcile our desire to broaden our access to aesthetic value with our desire to maintain and cultivate our meaningful aesthetic attachments. I motivate the alternative thought that having style is the aesthetic ideal. (shrink)

:A qualified pluralism is defended that recognizes value in a variety of forms of political theory and resists arguments that purport to show that one particular approach should occupy a privileged position. Against realists, it is argued that abstract analyses of political values that bracket a wide range of facts about people and their circumstances can be both coherent and important, whereas against those who think “ideal theory” or the identification of ultimate principles should come first, it is argued (...) that the case for always giving priority to either one of these is weak. (shrink)

THIS PAPER IS A DEFENSE OF AN OBJECTIVIST VERSION OF\nRODERICK FIRTH'S IDEAL OBSERVER THEORY OF ETHICS. IT\nANALYZES AND CRITIQUES A POWERFUL, RELATIVIZED IDEAL\nOBSERVER THEORY ADVANCED BY THOMAS CARSON.

This study aims at providing a global explanation of the good life or happiness according to Aristotle. By applying the method used in ethics by Aristotle, the specific content of happiness is determined, of which meditation is the essence, together with the practice of moral virtues. The article rests on a relatively new perspective, neither ‘exclusive’ nor ‘inclusive’, considering the results of each type of traditional interpretation, and shedding light upon the richness of all happiness’ dimensions.

I argue that recent virtue theories (including those of Hursthouse, Slote, and Swanton) face important initial difficulties in accommodating the supererogatory. In particular, I consider several potential characterizations of the supererogatory modeled upon these familiar virtue theories (and their accounts of rightness) and argue that they fail to provide an adequate account of supererogation. In the second half of the paper I sketch an alternative virtue-based characterization of supererogation, one that is grounded in the attitudes of virtuous ideal observers, (...) and that avoids the concerns raised in the first part of the paper. (shrink)

I express my dissatisfaction with the common ways to treat the semantic paradoxes. Not only do they give rise to revenge paradoxes, they ignore the wisdom contained in the ordinary reaction to paradoxes. I instead propose an account that vindicates the ordinary reaction to paradox by putting the blame on us philosophers. It is the wrong conception of what a valid inference is, one that is central to “the ideal of deductive logic” that gives rise to the problem. The (...) solution outlined gives us a new way to accept defeat in light of the paradoxes: the arguments that lead to them are based on valid forms of reasoning, but their conclusions are nonetheless rationally rejected. (shrink)

Probabilistic coherence is not an absolute requirement of rationality; nevertheless, it is an ideal of rationality with substantive normative import. An idealized rational agent who avoided making implicit logical errors in forming his preferences would be coherent. In response to the challenge, recently made by epistemologists such as Foley and Plantinga, that appeals to ideal rationality render probabilism either irrelevant or implausible, I argue that idealized requirements can be normatively relevant even when the ideals are unattainable, so long (...) as they define a structure that links imperfect and perfect rationality in a way that enables us to make sense of the notion of better approximations to the ideal. I then analyze the notion of approximation to the ideal of coherence by developing a generalized theory of belief functions that allows for incoherence, and showing how such belief functions can be ordered with regard to greater or lesser coherence. (shrink)

This paper has three aims. First, it argues that the present use of ‘ideal theory’ is unhelpful, and that an earlier and apparently more natural use focusing on perfection would be preferable. Second, it has tried to show that revision of the use of the term would better expose two distinctive normative issues, and illustrated that claim by showing how some contributors to debates about ideal theory have gone wrong partly through not distinguishing them. Third, in exposing those (...) two distinct normative issues, it has revealed a particular way in which ideal theory even under the more specific, revisionary definition will often be central to working out what to do in non-ideal circumstances. By clarifying the terms on which debates over ideal and non-ideal theory should take place, and highlighting the particular problems each deals with, it tries to clear the ground for turning to the actual problem, which is what to do in our non-ideal and often tragic circumstances. (shrink)

Kitcher's unification theory of explanation seems to suggest that only the most reductive accounts can legitimately be termed explanatory. This is not what we find in actual scientific practice. In this paper, I attempt to reconcile these ideas. I claim that Kitcher's theory picks out ideal explanations, but that our term explanation is used to cover other accounts that have a certain relationship with the ideal accounts. At times, versions and portions of ideal explanations can also be (...) considered explanatory. (shrink)

In this paper we introduce a tree-like forcing notion extending some properties of the random forcing in the context of 2κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^\kappa $$\end{document}, κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa $$\end{document} inaccessible, and study its associated ideal of null sets and notion of measurability. This issue was addressed by Shelah ), arXiv:0904.0817, Problem 0.5) and concerns the definition of a forcing which is κκ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa ^\kappa $$\end{document}-bounding, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,>\,$$\end{document}cov_λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\_\lambda $$\end{document}), arXiv:0904.0817, Problem 0.5), and in this paper we independently reprove this result by using a different type of construction. This also contributes to a line of research adressed in the survey paper :439–456, 2016). (shrink)

Let [NB]₁ denote the ideal generated by nonbounding c.e. degrees and NCup the ideal of noncuppable c.e. degrees. We show that both [NB]₁ ∪ NCup and the ideal generated by nonbounding and noncuppable degrees are new, in the sense that they are different from M, [NB]₁ and NCup—the only three known definable ideals so far.