It is shown to be consistent that the reals are covered by ℵ1 meagre sets yet there is a Baire class 1 function which cannot be covered by fewer than ℵ2 continuous functions. A new cardinal invariant is introduced which corresponds to the least number of continuous functions required to cover a given function. This is characterized combinatorially. A forcing notion similar to, but not equivalent to, superperfect forcing is introduced.

It is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

It is shown that the product of finitely many sequential, CLP-compact spaces is CLP-compact.

To any metric space it is possible to associate the cardinal invariant corresponding to the least number of rectifiable curves in the space whose union is not meagre. It is shown that this invariant can vary with the metric space considered, even when restricted to the class of convex subspaces of separable Banach spaces. As a corollary it is obtained that it is consistent with set theory that any set of reals of size ℵ 1 is meagre yet there are (...) ℵ 1 rectifiable curves in R 3 whose union is not meagre. The consistency of this statement when the phrase "rectifiable curves" is replaced by "straight lines" remains open. (shrink)

If F ⊆ NN is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable H ⊆ NN. no member of which is covered by finitely many functions from F, there is f ∈ F such that for all h ∈ H there are infinitely many integers k such that f(k) = h(k). However if V = L then there exists a coanalytic family of pairwise eventually different functions satisfying this strong maximality (...) condition. (shrink)

In this paper we show that it is consistent with ZFC that the cardinality of every maximal cofinitary group of Sym(ω) is strictly greater than the cardinal numbers o and a.

It is shown to be consistent that countable, Fréchet,α 1-spaces are first countable. The result is obtained by using a countable support iteration of proper partial orders of lengthω 2.

For a Polish group let be the minimal number of translates of a fixed closed nowhere dense subset of required to cover . For many locally compact this cardinal is known to be consistently larger than which is the smallest cardinality of a covering of the real line by meagre sets. It is shown that for several non-locally compact groups . For example the equality holds for the group of permutations of the integers, the additive group of a separable Banach (...) space with an unconditional basis and the group of homeomorphisms of various compact spaces. (shrink)

Various questions posed by P. Nyikos concerning ultrafilters on ω and chains in the partial order (ω, <*) are answered. The main tool is the oracle chain condition and variations of it.

The Mycielski ideal M k is defined to consist of all sets $A \subseteq ^{\mathbb{N}}k$ such that $\{f \upharpoonright X: f \in A\} \neq ^Xk$ for all X ∈ [N] ℵ 0 . It will be shown that the covering numbers for these ideals are all equal. However, the covering numbers of the closely associated Roslanowski ideals will be shown to be consistently different.

A strong coloring on a cardinal $\kappa $ is a function $f:[\kappa ]^2\to \kappa $ such that for every $A\subseteq \kappa $ of full size $\kappa $, every color $\unicode{x3b3} <\kappa $ is attained by $f\restriction [A]^2$. The symbol $$ \begin{align*} \kappa\nrightarrow[\kappa]^2_{\kappa} \end{align*} $$ asserts the existence of a strong coloring on $\kappa $.We introduce the symbol $$ \begin{align*} \kappa\nrightarrow_p[\kappa]^2_{\kappa} \end{align*} $$ which asserts the existence of a coloring $f:[\kappa ]^2\to \kappa $ which is strong over a partition $p:[\kappa ]^2\to (...) \theta $. A coloring f is strong over p if for every $A\in [\kappa ]^{\kappa }$ there is $i<\theta $ so that for every color $\unicode{x3b3} <\kappa $ is attained by $f\restriction )$.We prove that whenever $\kappa \nrightarrow [\kappa ]^2_{\kappa }$ holds, also $\kappa \nrightarrow _p[\kappa ]^2_{\kappa }$ holds for an arbitrary finite partition p. Similarly, arbitrary finite p-s can be added to stronger symbols which hold in any model of ZFC. If $\kappa ^{\theta }=\kappa $, then $\kappa \nrightarrow _p[\kappa ]^2_{\kappa }$ and stronger symbols, like $\operatorname {Pr}_1_p$ or $\operatorname {Pr}_0_p$, also hold for an arbitrary partition p to $\theta $ parts.The symbols $$ \begin{gather*} \aleph_1\nrightarrow_p[\aleph_1]^2_{\aleph_1},\;\;\; \aleph_1\nrightarrow_p[\aleph_1\circledast \aleph_1]^2_{\aleph_1},\;\;\; \aleph_0\circledast\aleph_1\nrightarrow_p[1\circledast\aleph_1]^2_{\aleph_1}, \\ \operatorname{Pr}_1_p,\;\;\;\text{ and } \;\;\; \operatorname{Pr}_0_p \end{gather*} $$ hold for an arbitrary countable partition p under the Continuum Hypothesis and are independent over ZFC $+ \neg $ CH. (shrink)

We present some techniques in c.c.c. forcing, and apply them to prove consistency results concerning the isomorphism and embeddability relations on the family of ℵ 1 -dense sets of real numbers. In this direction we continue the work of Baumgartner [2] who proved the axiom BA stating that every two ℵ 1 -dense subsets of R are isomorphic, is consistent. We e.g. prove Con). Let K H , be the set of order types of ℵ 1 -dense homogeneous subsets of (...) R with the relation of embeddability. We prove that for every finite model L , : Con iff L is a distributive lattice. We prove that it is consistent that the Magidor-Malitz language is not countably compact. We deal with the consistency of certain topological partition theorems. E.g. We prove that MA is consistent with the axiom OCA which says: “If X is a second countable space of power ℵ 1 , and { U 0 ,\h.;, U n−1 } is a cover of D ▪ X x X -} x,x> ¦ x ϵ X } consisting of symmetric open sets, then X can be partitioned into { X i \brvbar; i ϵ ω } such that for every i ϵ ω there is l such that D ⊇ U l ”. We also prove that MA+OCA [xrArr] 2 ℵ 0 = ℵ 2. (shrink)

By B2 we denote the σ-ideal of all subsets A of the Cantor set {0,1}ω such that for every infinite subset T of ω the restriction A∣{0,1}T is a proper subset of {0,1}T. In this paper we investigate set theoretical properties of this and similar ideals.

By $\mathfrak{B}_2$ we denote the $\sigma$-ideal of all subsets $A$ of the Cantor set $\{0,1\}^\omega$ such that for every infinite subset $T$ of $\omega$ the restriction $A\mid\{0,1\}^T$ is a proper subset of $\{0,1\}^T$. In this paper we investigate set theoretical properties of this and similar ideals.

This article, first published in Russian in 1984 in Sign Systems Studies, introduces the concept of semiosphere and describes its principal attributes. Semiosphere is the semiotic space, outside of which semiosis cannot exist. The ensemble of semiotic formations functionally precedes the singular isolated language and becomes a condition for the existence of the latter. Without the semiosphere, language not only does not function, it does not exist. The division between the core and the periphery is a law of the internal (...) organisation of the semiosphere. There exists boundary between the semiosphere and the non- or extra-semiotic space that surrounds it. The semiotic border is represented by the sum of bilingual translatable “filters”, passing through which the text is translated into another language (or languages), situated outside the given semiosphere. The levels of the semiosphere comprise an inter-connected group of semiospheres, each of them being simultaneously both participant in the dialogue (as part of the semiosphere) and the space of dialogue (the semiosphere as a whole). (shrink)

Nakba is ignored in Western philosophy encyclopedias, and the notion of genocide is rarely explained. In turn, there is much talk about the Holocaust.

There is widespread agreement that the European Union is presently suffering from a lack of social justice. Yet there is significant disagreement about what the relevant injustice consists in: Federalists believe the EU can only remedy its justice deficit through the introduction of direct interpersonal transfers between people living in separate states. Intergovernmentalists believe the justice-related purpose of the EU is to enable states to cooperate fairly, and to remain internally just and democratic in the face of increased global pressure (...) on welfare states. I suggest that despite their fundamental differences, many of the most reasonable and prominent philosophical accounts of social justice in the EU nonetheless converge in their institutional prescriptions. In particular, they may each serve as a justificatory basis for introducing the European social minimum, an EU-wide income support scheme. (shrink)

This article by Juri Lotman from the third volume of Trudy po znakovym sistemam (Sign Systems Studies) in 1967, deals with the problem of artistic modelling. The general working questions are whether art displays any characteristic traits that are common for all modelling systems and which could be the specific traits that can distinguish art from other modelling systems. Art is seen as a secondary modelling system, more precisely, as a play-type model, which is characterised simultaneously by practical and conventional (...) behaviour and constant awareness of the possibility of alternate meanings to the one that is currently being perceived. At the same time art has play-like elements but is not the same as play, since play is inherently rule-bound, whereas art is a more flexible model thepurpose of which is truth. Art is a special type of modelling system, since it is on one hand suitable for storing very large amount of complex information, but onthe other hand it can increase the stored information and transform the consumer. (shrink)

Many attempts have been made to solve Hume's problem. However, the assumptions leading to the problem have remained largely unnoticed. Moreover, since Goodman introduced the predicate "grue", philosophers without relevant mathematical education have been confused. In addition, various delusive arguments from convergence have been presented. In this book, it is maintained that knowledge has to be feasible and relevant and that several solutions fail to meet that demand. It is argued that the crucial presupposition of the problem of induction is (...) that clairvoyance is impossible and that this presupposition is unproven. Generalized Goodman predicates are introduced. To criticize arguments from convergence, the notion of "undecided game" is introduced. A relationship between Zeno's paradox and the problem of induction is revealed. A distinction between "do not know" and "cannot know" is consistently held. It is concluded that, as yet, we do not know the future and that it is impossible to prove that it is impossible to know the future. This book should be useful to professionals in epistemology and philosophy of science, and might be of interest to logicians and mathematicians. (shrink)

Tõde või eimiski [= Truth or Nothingness]. A collection of philosophical essays 1990-2021. In Estonian. -/- Kogumikku hoolikalt valitud tekstid on ühelt poolt loomingulised, lugejat intrigeerivad ning interdistsiplinaarsed – kõige rohkem põimitakse filosoofilisi arutlusi psühholoogilistega. Kuid teisest küljest on esseed filosoofiliselt ranged, demonstreerides oskust jääda ka rakenduslikes teemaarendustes üdini filosoofiks. Raamatus leidub nii filosoofia olemuse üle arutlevaid tekste, kaasahaaravaid filosoofia suurkujude tõlgendusi, põhjalikult käsitletakse ka praktilise filosoofia alla kuuluvaid teemasid kuni meie kaasaja poliitilise olukorra diagnoosi ja kriitikani välja. Raamatu lõpus (...) on intervjuu väljaandjaga. (shrink)

Spontaneous Infra-Slow Fluctuations of the human EEG were discovered 60 years ago when appropriate amplifiers for their recordings were designed. To avoid skin-related artifacts the recording of EEG-ISFs required puncturing the skin under the electrode. In the beginning of the 21st century the interest in EEG-ISFs was renewed with the appearance of commercially available DC-coupled amplified and by observation of ISFs of the blood oxygen level–dependent functional magnetic resonance imaging signal at a similar frequency. The independent components of irregular EEG-ISFs (...) were shown to correlate with BOLD signals which in turn were driven by changes in arousal level measured by galvanic skin response, pupil size and HRV. There is no consensus regarding the temporal organization of EEG-ISFs: some studies emphasize the absence of peaks on EEG-ISFs spectra, some studies report prominent oscillations with frequency around 0.1 or 0.02 Hz, while some emphasize multiple discrete infraslow oscillations. No studies used parameters of EEG-ISFs as neuromarkers to discriminate psychiatric patients from healthy controls. Finally, a set of working hypotheses is suggested that must be tested in future research to solve the enigma of EEG-ISFs. (shrink)