The cohesive principle and the Bolzano-Weierstra{\ss} principle

The aim of this paper is to determine the logical and computational strength of instances of the Bolzano-Weierstra{\ss} principle (BW) and a weak variant of it. We show that BW is instance-wise equivalent to the weak K\"onig's lemma for $\Sigma^0_1$-trees ($\Sigma^0_1$-WKL). This means that from every bounded sequence of reals one can compute an infinite $\Sigma^0_1$-0/1-tree, such that each infinite branch of it yields an accumulation point and vice versa. Especially, this shows that the degrees d >> 0' are exactly those containing an accumulation point for all bounded computable sequences. Let BW_weak be the principle stating that every bounded sequence of real numbers contains a Cauchy subsequence (a sequence converging but not necessarily fast). We show that BW_weak is instance-wise equivalent to the (strong) cohesive principle (StCOH) and - using this - obtain a classification of the computational and logical strength of BW_weak. Especially we show that BW_weak does not solve the halting problem and does not lead to more than primitive recursive growth. Therefore it is strictly weaker than BW. We also discuss possible uses of BW_weak.Comment: corrected typos, slightly improved presentatio

Generalized cohesiveness

We study some generalized notions of cohesiveness which arise naturally in connection with effective versions of Ramsey's Theorem. An infinite set $A$ of natural numbers is $n$--cohesive (respectively, $n$--r--cohesive) if $A$ is almost homogeneous for every computably enumerable (respectively, computable) $2$--coloring of the $n$--element sets of natural numbers. (Thus the $1$--cohesive and $1$--r--cohesive sets coincide with the cohesive and r--cohesive sets, respectively.) We consider the degrees of unsolvability and arithmetical definability levels of $n$--cohesive and $n$--r--cohesive sets. For example, we show that for all $n \ge 2$, there exists a $\Delta^0_{n+1}$ $n$--cohesive set. We improve this result for $n = 2$ by showing that there is a $\Pi^0_2$ $2$--cohesive set. We show that the $n$--cohesive and $n$--r--cohesive degrees together form a linear, non--collapsing hierarchy of degrees for $n \geq 2$. In addition, for $n \geq 2$ we characterize the jumps of $n$--cohesive degrees as exactly the degrees {\bf \geq \jump{0}{(n+1)}} and show that each $n$--r--cohesive degree has jump {\bf > \jump{0}{(n)}}

Iterative forcing and hyperimmunity in reverse mathematics

The separation between two theorems in reverse mathematics is usually done by constructing a Turing ideal satisfying a theorem P and avoiding the solutions to a fixed instance of a theorem Q. Lerman, Solomon and Towsner introduced a forcing technique for iterating a computable non-reducibility in order to separate theorems over omega-models. In this paper, we present a modularized version of their framework in terms of preservation of hyperimmunity and show that it is powerful enough to obtain the same separations results as Wang did with his notion of preservation of definitions.Comment: 15 page

-Generic Computability, Turing Reducibility and Asymptotic Density

Generic computability has been studied in group theory and we now study it in the context of classical computability theory. A set A of natural numbers is generically computable if there is a partial computable function f whose domain has density 1 and which agrees with the characteristic function of A on its domain. A set A is coarsely computable if there is a computable set C such that the symmetric difference of A and C has density 0. We prove that there is a c.e. set which is generically computable but not coarsely computable and vice versa. We show that every nonzero Turing degree contains a set which is not coarsely computable. We prove that there is a c.e. set of density 1 which has no computable subset of density 1. As a corollary, there is a generically computable set A such that no generic algorithm for A has computable domain. We define a general notion of generic reducibility in the spirt of Turing reducibility and show that there is a natural order-preserving embedding of the Turing degrees into the generic degrees which is not surjective

Freely forming groups: trying to be rare

A simple weakly frequency dependent model for the dynamics of a population with a finite number of types is proposed, based upon an advantage of being rare. In the infinite population limit, this model gives rise to a non-smooth dynamical system that reaches its globally stable equilibrium in finite time. This dynamical system is sufficiently simple to permit an explicit solution, built piecewise from solutions of the logistic equation in continuous time. It displays an interesting tree-like structure of coalescing components

Asymptotic density and the Ershov hierarchy

We classify the asymptotic densities of the $\Delta^0_2$ sets according to their level in the Ershov hierarchy. In particular, it is shown that for $n \geq 2$, a real $r \in [0,1]$ is the density of an $n$-c.e.\ set if and only if it is a difference of left-$\Pi_2^0$ reals. Further, we show that the densities of the $\omega$-c.e.\ sets coincide with the densities of the $\Delta^0_2$ sets, and there are $\omega$-c.e.\ sets whose density is not the density of an $n$-c.e. set for any $n \in \omega$.Comment: To appear in Mathematical Logic Quarterl

EVIDENCE OF COMMUNAL OVIPOSITION AND NEST ABANDONMENT IN THE NORTHERN TWO-LINED SALAMANDER (EURYCEA BISLINEATA, (GREEN, 1818)) IN NORTHEASTERN CONNECTICUT

Most plethodontid salamanders oviposit their eggs in an individual nest and attend the clutch until hatching. Here, we describe aspects of the reproduction of Eurycea bislineata (Northern Two-lined Salamander) from three field sites in northeastern Connecticut that contrast with the typical plethodontid reproductive behavior. Rocks used as oviposition sites contained up to 296 eggs, with an average of more than 100. These numbers exceed the maximum ovarian egg counts for this species, indicating that communal oviposition is common. The lack of correlation between rock size and number of eggs, as well as the lack of discrete clutches when eggs are laid in large clusters, suggests that communal oviposition may be caused by something other than nest site limitation. Additionally, the rate of maternal attendance at nests was low. Thus, communal oviposition with high rates of nest abandonment is the dominant reproductive strategy in E. bislineata at these sites

Use of a novel collagen matrix with oriented pore structure for muscle cell differentiation in cell culture and in grafts

Tissue engineering of skeletal muscle from cultured cells has been attempted using a variety of synthetic and natural macromolecular scaffolds. Our study describes the application of artificial scaffolds (collagen sponges, CS) consisting of collagen-I with parallel pores (width 20–50 μm) using the permanent myogenic cell line C2C12. CS were infiltrated with a high-density cell suspension, incubated in medium for proliferation of myoblasts prior to further culture in fusion medium to induce differentiation and formation of multinucleated myotubes. This resulted in a parallel arrangement of myotubes within the pore structures. CS with either proliferating cells or with myotubes were grafted into the beds of excised anterior tibial muscles of immunodeficient host mice. The recipient mice were transgenic for enhanced green fluorescent protein (eGFP) to determine a host contribution to the regenerated muscle tissue. Histological analysis 14–50 days after surgery showed that donor muscle fibres had formed in situ with host contributions in the outer portions of the regenerates. The function of the regenerates was assessed by direct electrical stimulation which resulted in the generation of mechanical force. Our study demonstrated that biodegradable CS with parallel pores support the formation of oriented muscle fibres and are compatible with force generation in regenerated muscle

Paradise Lost? Postwar Memory of Polish Jewish Survival in the Soviet Union

The vast majority of Polish Jews who survived the Holocaust owed their survival to their flight or deportation to the Soviet Union. Yet, their story figured little in early postwar commemoration in the Displaced Persons camps of Germany and in survivor communities in Poland and elsewhere. Using new source material to provide an internal perspective on these communities, the authors argue that the downplaying of the Soviet experience in public memory was politically and ideologically motivated and was determined by the larger context of postwar politic