Related papers: On two problems of Erdos and Hechler: New methods …

We prove (ZF+DC) e.g. : if mu =|H(mu)| then mu^+ is regular non measurable. This is in contrast with the results for mu = aleph_{omega} on measurability see Apter Magidor [ApMg]

We use the core model for sequences of measures to prove a new lower bound for the consistency strength of the failure of the SCH: THEOREM (i) If there is a singular strong limit cardinal $\kappa$ such that $2^\kappa > kappa^+$ then there…

We further investigate the class of models of a strongly dependent (first order complete) theory T, continuing math.LO/0406440. If |A|+|T|<= mu, I subseteq C, |I| >=beth_{|T|^+}(mu) then some J subseteq I of cardinality mu^+ is an…

If we replace first order logic by second order logic in the original definition of G\"odel's inner model $L$, we obtain HOD. In this paper we consider inner models that arise if we replace first order logic by a logic that has some, but…

Magnitude is a numerical invariant of finite metric spaces, recently introduced by T. Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of topological spaces. It has been extended…

Answering a problem of Eklof and Mekler, we show that there is a reflexive group of cardinality >= first measurable.

We show that an infinite family of odd complex 2-dimensional Galois representations ramified at 5 having nonsolvable projective image are modular, thereby verifying Artin's conjecture for a new case of examples. Such a family contains the…

We prove the consistency of the statement $\mathfrak{u}_{\aleph_\omega}<2^{\aleph_\omega}$. We show that the consistency strength of this statement is exactly a measurable cardinal $\mu$ so that $o(\mu)=\mu^{++}$.

We study the topological $\mu$-calculus, based on both Cantor derivative and closure modalities, proving completeness, decidability and FMP over general topological spaces, as well as over $T_0$ and $T_D$ spaces. We also investigate…

This is the first part of a work devoted to the study of linear Mahler systems in several variables from the perspective of transcendence and algebraic independence. We prove two main results concerning systems that are regular singular at…

The topic of this paper is the Finiteness Conjecture for minimally unsatisfiable clause-sets (MUs), stating that for each fixed deficiency (number of clauses minus number of variables) there are only finitely many patterns, given a certain…

We prove that, e.g., if mu >cf(mu)= aleph_0 and mu>2^{aleph_0} and every stationary family of countable subsets of mu^+ reflect in some subset of mu^+ of cardinality aleph_1, then the SCH for mu^+ (moreover, for mu^+, any scale for mu^+ has…

Strongly bounded groups are those groups for which every action by isometries on a metric space has orbits of finite diameter. Many groups have been shown to have this property, and all the known infinite examples so far have cardinality at…

We present a new, scalable alternative to the structured singular value, which we call $\nu$, provide a convex upper bound, study their properties and compare them to $\ell_1$ robust control. The analysis relies on a novel result on the…

The intractability of any problem and the randomness of its solutions have an obvious intuitive connection. However, the challenge till now has been that there is no practical way to firmly establish if the solution to a problem is actually…

We show, assuming the consistency of one measurable cardinal, that it is consistent for there to be exactly kappa+ many normal measures on the least measurable cardinal kappa. This answers a question of Stewart Baldwin. The methods…

We define a weak iterability notion that is sufficient for a number of arguments concerning $\Sigma_1$-definability at uncountable regular cardinals. In particular we give its exact consistency strength firstly in terms of the second…

We provide a non-trivial measure of irrationality for a class of Mahler numbers defined with infinite products which cover the Thue-Morse constant.

Assume L(\mathbb{R},\mu) satisfies ZF+DC+\Theta>\omega_2 + \mu is a normal fine measure on \powerset_{\omega_1}(\mathbb{R}). The main result of this paper is the characterization theorem of L(\mathbb{R},\mu) which states that…

We prove the consistency of a singular cardinal $\lambda$ with small value of the ultrafilter number $u_\lambda$, and arbitrarily large value of $2^\lambda$.