IL MOSTRO E L'EROE. Quando Pomponio Algieri da Nola, all’età di soli 24 anni, viene bruciato vivo a Roma in piazza Navona, Giordano Bruno di anni ne ha appena otto. Oltre che per la giovane età del condannato, l’esecuzione è insolita anche per il luogo e il metodo scelto dall’Inquisizione: anziché le solite fascine, per alimentare il fuoco viene approntato un pentolone di pece, olio e trementina, nel quale viene immersa la povera vittima.

Betrachtungen über die Erkenntnis,die Wahrheit und die Ideen.--Übber die Verbesserung der ersten Philosophie und den Begriff der Substanz.--Neues System der Natur und der Verbindung der Substanzen sowie dier Vereinigung zwischen Seel und Körper.--Über den ersten Ursprung der Dinge.--Betrachtungen über die Lehre von einem einzigen allumfassenden Geiste.

The apolipoprotein E gene plays an important role in the pathogenesis of Alzheimer's disease , and amyloid plaque comprised mostly of the amyloid-beta peptide ) is one of the major hallmarks of AD. However, the relationship between these two important molecules is poorly understood. We examined how A treatment affects APOE expression in cultured cells and tested the role of the transcription factor NF-B in APOE gene regulation. To delineate NF-B's role, we have characterized a 1098 nucleotide segment containing the (...) 5'-flanking region of the human APOE gene . Sequence analysis of this region suggests the presence of two potential NF-B elements. To demonstrate promoter activity, the region was cloned upstream of a promoterless luciferase gene. This segment was able to drive expression of luciferase in transient transfections of human fetal glial cells. Promoter activity was stimulated twofold by A treatment. Pretreatment with double-stranded DNA decoy oligonucleotides against NF-B reduced A stimulation. Deletion and mutagenetic analyses demonstrated that the distal NF-B element was functional and showed a strong DNA-protein complex band in gel shift analysis, similar to that from control NF-B consensus element. An anti-inflammatory and anti-NF-B drug, sodium salicylate, significantly blocked A-induced APOE promoter function. Our data provide evidence that upregulation of APOE by A in astroglial cells is mediated by an NF-B-element present in the 5'-flanking region of the APOE gene. (shrink)

A pathogenic connection between autoreactive T cells, fungal infection, and carcinogenesis has been demonstrated in studies of human autoimmune polyendocrinopathy-candidiasis-ectodermal dystrophy as well as in a mouse model in which kinase-dead Ikkα knock-in mice develop impaired central tolerance, autoreactive T cell–mediated autoimmunity, chronic fungal infection, and esophageal squamous cell carcinoma, which recapitulates APECED. IκB kinase α is one subunit of the IKK complex required for NF-κB activation. IKK/NF-κB is essential for central tolerance establishment by regulating the development of medullary thymic (...) epithelial cells that facilitate the deletion of autoreactive T cells in the thymus. In this review, we extensively discuss the pathogenic roles of inborn errors in the IKK/NF-κB loci in the phenotypically related diseases APECED, immune deficiency syndrome, and severe combined immunodeficiency; differentiate how IKK/NF-κB components, through mTEC, T cells/leukocytes, or epithelial cells, contribute to the pathogenesis of infectious diseases, autoimmunity, and cancer; and highlight the medical significance of IKK/NF-κB in these diseases. IKK/NF-κB regulates the expression of many genes that encode proteins involved in many crucial biological functions, such as immunity, tissue homeostasis, and fungal/bacterial/viral infections. Also, IKKα plays anti-tumor activities in many organs independently of NF-κB pathways. Thus, an inborn error in one of these gene loci can cause severe human diseases through these complicated mechanisms. (shrink)

We give a necessary and sufficient condition in order that a type-shifting automorphism be constructed on a model of the Theory of Simple Types (TST) by forcing. Namely it is proved that, if for every n ≥ 1 there is a model of TST in the ground model M of ZFC that contains an n-extendible coherent pair, then there is a generic extension M[G] of M that contains a model of TST with a type-shifting automorphism, and hence M[G] contains a (...) model of NF. The converse holds trivially. It is also proved that there exist models of TST containing l-extendible coherent pairs. (shrink)

We show that, if non-uniform impredicative stratified comprehension is assumed, Feferman's theories of explicit mathematics are consistent with a strong power type axiom. This result answers a problem, raised by Jäger. The proof relies upon an interpretation into Quine's set theory NF with urelements.

Both Notch and NFκB signaling pathways are well‐known for regulating proliferation, differentiation and apoptosis. Recent studies have presented several lines of evidence supporting an integration of the Notch and NFκB signaling pathways in differentiation/maturation of a diverse range of cell types. It is notable that Notch and NFκB signaling pathways share many common features: (i) both are activated by common stimuli such as TNF‐α and hypoxia, (ii) activated Notch (NICD) and NFκB mediate transcription by regulating corepressors such as SMRT/N‐COR, and (...) (iii) both regulate similar target genes such as Hes‐1 and IκBα. This review expands on how the collaboration between these pathways may play an important role in the CNS. We will speculate on the mechanisms by which Notch and NFκB signaling may collaborate to regulate stem cell renewal and differentiation during brain development and function. BioEssays 29:1039–1047, 2007. © 2007 Wiley Periodicals, Inc. (shrink)

We identify complete fragments of the simple theory of types with infinity and Quine’s new foundations set theory. We show that TSTI decides every sentence ϕ in the language of type theory that is in one of the following forms: ϕ=∀x1r1⋯∀xkrk∃y1s1⋯∃ylslθ where the superscripts denote the types of the variables, s1>⋯>sl, and θ is quantifier-free, ϕ=∀x1r1⋯∀xkrk∃y1s⋯∃ylsθ where the superscripts denote the types of the variables and θ is quantifier-free. This shows that NF decides every stratified sentence ϕ in the language (...) of set theory that is in one of the following forms: ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns distinct values to all of the variables y1,…,yl, ϕ=∀x1⋯∀xk∃y1⋯∃ylθ where θ is quantifier-free and ϕ admits a stratification that assigns the same value to all of the variables y1,…,yl. (shrink)

An instance of Stratified Comprehension ∀x₁ … ∀x n ∃y∀x (x ∈ y ↔ φ(x, x₁, …, x n )) is called strictly impredicative iff, under minimal stratification, the type of x is 0. Using the technology of forcing, we prove that the fragment of NF based on strictly impredicative Stratified Comprehension is consistent. A crucial part in this proof, namely showing genericity of a certain symmetric filter, is due to Robert Solovay. As a bonus, our interpretation also satisfies some (...) instances of Stratified Comprehension which are not strictly impredicative. For example, it verifies existence of Frege natural numbers. Apparently, this is a new subsystem of NF shown to be consistent. The consistency question for the whole theory NF remains open (since 1937). (shrink)

The main feature of NF/NFU is the notion of stratification, which sets it apart from other set theories. We define stratification and prove constructively that every stratified formula has the (unique) least assignment of types. The basic notion of stratification is concerned only with variables, but we extend it to abstraction terms in order to simplify further development. We reflect on nested abstraction terms, proving that they get the expected types. These extensions enable us to check whether some complex formula (...) is stratified without rewriting it in the basic language. We also introduce natural numbers and a variant of the axiom of infinity, in order to precisely introduce type level ordered pairs, which are crucial in simplifying the definitions in the last part of the article. Using these notions we can easily define the sets of ordinal and cardinal numbers, which we show at the end of the article. The same approach can be readily applied to NF. (shrink)

The theory New Foundations of Quine was introduced in [14]. This theory is finitely axiomatizable as it has been proved in [9]. A similar result is shown in [8] using a system called K. Particular subsystems of NF, inspired by [8] and [9], have models in ZF. Very little is known about subsystems of NF satisfying typical properties of ZF; for example in [11] it is shown that the existence of some sets which appear naturally in ZF is an axiom (...) independent from NF . Here we discuss a model of subsystems of NF in which there is a set which is a model of ZF. MSC: 03E70. (shrink)

An ω-model (a model in which all natural numbers are standard) of the predicative fragment of Quine's set theory "New Foundations" (NF) is constructed. Marcel Crabbe has shown that a theory NFI extending predicative NF is consistent, and the model constructed is actually a model of NFI as well. The construction follows the construction of ω-models of NFU (NF with urelements) by R. B. Jensen, and, like the construction of Jensen for NFU, it can be used to construct α-models for (...) any ordinal α. The construction proceeds via a model of a type theory of a peculiar kind; we first discuss such "tangled type theories" in general, exhibiting a "tangled type theory" (and also an extension of Zermelo set theory with Δ 0 comprehension) which is equiconsistent with NF (for which the consistency problem seems no easier than the corresponding problem for NF (still open)), and pointing out that "tangled type theory with urelements" has a quite natural interpretation, which seems to provide an explanation for the more natural behaviour of NFU relative to the other set theories of this kind, and can be seen anachronistically as underlying Jensen's consistency proof for NFU. (shrink)

Partial models of the theory New Foundations (NF) introduced by Quine have already appeared in the literature, but in every model the membership set of NF is missing. On the other hand, Jensen showed that "NF + Urelements" is consistent with respect to ZF and, in the model built there, the membership set of the theory exists. Here we build a partial model of NF from the one of Jensen in which the membership set exists.

v. 1. Schriften zur Anthropologie und Geschichte -- v. 2. Schriften zur Altertumskunde und Ästhetik. Die Vasken -- v. 3. Schriften zur Sprachphilosophie -- v. 4. Schriften zur politik und zum bildungswesen -- v. 5. Kleine Schriften, autobiographisches, Dichtungen, Briefe, Kommentare und Ammerkungen zu Band I-V, Anhang.

The aging process involves changes in immune regulation, i.e. adaptive immunity declines whereas innate immunity becomes activated. NF‐κB signaling is the master regulator of the both immune systems. Two recent articles highlight the role of the NF‐κB system in aging and immune responses. Adler et al1 showed that the NF‐κB binding domain is the genetic regulatory motif which is most strongly associated with the aging process. Kwon et al2 studying HIV‐1 infection and subsequent immune deficiency process demonstrated that HIV‐1 Tat (...) protein binds to SIRT1 protein, a well‐known longevity factor, and inhibits the SIRT1‐mediated deacetylation of the p65 component of the NF‐κB complex. As a consequence, the transactivation efficiency of the NF‐κB factor was greatly potentiated, leading to the activation of immune system and later to the decline of adaptive immunity. These observations support the scenario where immune responses and aging process can be enforced by the potentiation of NF‐κB transactivation efficiency. Longevity factors, such as SIRT1 and its activators, might regulate the efficiency of the NF‐κB signaling, the major outcome of which is inflamm‐aging via proinflammatory responses. BioEssays 30:939–942, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

The transcription factor NF‐κB (p65/p50) plays a central role in the coordination of cellular responses by activating the transcription of numerous target genes. The precise role of the dynamics of NF‐κB signalling in regulating gene expression is still an open question. Here, we show that besides external stimulation intracellular parameters can influence the dynamics of NF‐κB. By applying mathematical modelling and bifurcation analyses, we show that NF‐κB is capable of exhibiting different types of dynamics in response to the same stimulus. (...) We identified the total NF‐κB concentration and the IκBα transcription rate constant as two critical parameters that modulate the dynamics and the fold change of NF‐κB. Both parameters might vary as a result of cell‐to‐cell variability. The regulation of the IκBα transcription rate constant, e.g. by co‐factors, provides the possibility of regulating the NF‐κB dynamics by crosstalk. (shrink)

Quine’s “New Foundations” (NF) was first presented in Quine [1937] and later on in Quine [1963]. Ernst Specker [1958, 1962], building upon a previous result of Ehrenfeucht and Mostowski [1956], showed that NF is consistent if and only if there is a model of the Theory of Negative (and positive) Types (TNT) with full extensionality that admits of a “shifting automorphism,” but the existence of a such a model remains an open problem.

A paper by Beneš, published in 1954, was an attempt to prove the consistency of $\mathsf{NF}$ via a partial model of Hailperin’s finite axiomatization of $\mathsf{NF}$. Here, I offer an analysis of Beneš’s proof in a De Giorgi-style setting for set theory. This approach leads to an abstract version of Beneš’s theorem that emphasizes the monotone and invariant content of the axioms proved to be consistent, in a sense of monotony and invariance that this paper intends to state rigorously and (...) to help clarify. Moreover, some tentative speculation will be made about possible developments of the topic in the following two directions: which set theories can be proved to be consistent via Beneš-like constructions, and how can we elaborate on Beneš’s model to get a consistency proof for full $\mathsf{NF}$? (shrink)

Section 1 is devoted to the study of countable recursively saturated models with an automorphism moving every non-algebraic point. We show that every countable theory has such a model and exhibit necessary and sufficient conditions for the existence of automorphisms moving all non-algebraic points. Furthermore we show that there are many complete theories with the property that every countable recursively saturated model has such an automorphism. In Section 2 we apply our main theorem from Section 1 to models of Quine's (...) set theory New Foundations (NF) to answer an old consistency question. If NF is consistent, then it has a model in which the standard natural numbers are a definable subclass N of the model's set of internal natural numbers Nn. In addition, in this model the class of wellfounded sets is exactly $\bigcup_{n\in \mathbb{N}}\mathscr{P}^n(\varnothing)$. (shrink)

Abstractc‐Rel is a proto‐oncogene first identified as the cellular counterpart of the v‐Rel oncogene derived from the avian reticuloendotheliosis retrovirus (REV‐T). It was subsequently discovered that c‐Rel belongs to the NF‐κB/Rel transcription factor family whose members share a common DNA recognition motif and similar signaling pathways. Despite the similarities, however, each NF‐κB/Rel member possesses unique properties with regard to tissue expression pattern, response to receptor signals and target gene specificity. These differences are fairly evident from the non‐redundant phenotypes exhibited by (...) individual NF‐κB/Rel knockout mice. Hence the work described in this review will compare and contrast the various physiological functions of c‐Rel to those of other NF‐κB members, particularly with respect to the regulation of proliferation, survival and effector functions in multiple hematopoietic and immunological cell types. The study of c‐Rel knockout mice in several disease models will also be discussed as they reveal an important role for c‐Rel in response to allergens, auto‐antigens, allo‐antigens and pathogenic infection. BioEssays 25:767–780, 2003. © 2003 Wiley Periodicals, Inc. (shrink)

It is shown that, according to NF, many of the assertions of ordinal arithmetic involving the T-function which is peculiar to NF turn out to be equivalent to the truth-in-certain-permutation-models of assertions which have perfectly sensible ZF-style meanings, such as: the existence of wellfounded sets of great size or rank, or the nonexistence of small counterexamples to the wellfoundedness of ∈. Everything here holds also for NFU if the permutations are taken to fix all urelemente.

We prove that if G is a Δ 0 -definable function on the natural numbers and F = Π i = 0 n G , then F is also Δ 0 -definable. Moreover, the inductive properties of F can be proved inside the theory IΔ 0.