Related papers: Tameness from two successive good frames

We investigate the problem of when $\leq\lambda$--support iterations of $<\lambda$--complete notions of forcing preserve $\lambda^+$. We isolate a property -- {\em properness over diamonds} -- that implies $\lambda^+$ is preserved and show…

We define a reasonably well-behaved class of ultraimaginaries, i.e.\ classes modulo invariant equivalence relations, called {\em tame}, and establish some basic simplicity-theoretic facts. We also show feeble elimination of supersimple…

We study the model theory of vector spaces with a bilinear form over a fixed field. For finite fields this can be, and has been, done in the classical framework of full first-order logic. For infinite fields we need different logical…

The third author has shown that Shelah's eventual categoricity conjecture holds in universal classes: class of structures closed under isomorphisms, substructures, and unions of chains. We extend this result to the framework of…

We extend and improve the result of Makkai and Par\'e that the powerful image of any accessible functor F is accessible, assuming there exists a sufficiently large strongly compact cardinal. We reduce the required large cardinal assumption…

We present a version with non-definable forcing notions of Shelah's theory of iterated forcing along a template. Our main result, as an application, is that, if $\kappa$ is a measurable cardinal and $\theta<\kappa<\mu<\lambda$ are…

We like to develop model theory for $T$, a complete theory in $\mathbb{L}_{\theta,\theta}(\tau)$ when $\theta$ is a compact cardinal. By [Sh:300a] we have bare bones stability and it seemed we can go no further. Dealing with ultrapowers…

We prove that the category of countable Tate modules over an arbitrary discrete ring embeds fully faithfully into that of condensed modules. If the base ring is of finite type, we characterize the essential image as generated by the free…

We show that in the theory ZF + DC + for every cardinal {\lambda}, the set of infinite subsets of {\lambda} is well-ordered (i.e., Shelah's AX4), the {\theta}-function measuring the surjective size of the powersets P({\kappa}) can take…

Assuming the existence of a monster model, tameness and continuity of nonsplitting in an abstract elementary class (AEC), we extend known superstability results: let $\mu>LS({\bf K})$ be a regular stability cardinal and let $\chi$ be the…

We investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent…

We consider a fourth order evolution equation involving a singular nonlinear term $\frac{\lambda}{(1-u)^{2}}$ in a bounded domain $\Omega\subset\R^{n}$. This equation arises in the modeling of microelectromechanical systems. We first…

We prove that in a theory $T$ stable over a predicate $P$, for any $\lambda > |T|$, there is a $\lambda$-prime model over any complete set A with a $\lambda$-saturated $P$-part.

We show that supercompactness and strong compactness can be equivalent even as properties of pairs of regular cardinals. Specifically, we show that if V models ZFC + GCH is a given model (which in interesting cases contains instances of…

We present reasons for developing a theory of forcing notions which satisfy the properness demand for countable models which are not necessarily elementary submodels of some (H(chi), in). This leads to forcing notions which are…

For an arbitrary finite dimensional algebra $\Lambda$, we prove that any wide subcategory of $\mathsf{mod} \Lambda$ satisfying a certain finiteness condition is $\theta$-semistable for some stability condition $\theta$. More generally, we…

Given a special biserial algebra $\Lambda$ over an algebraically closed field, let $\mathrm{rad}_\Lambda$ denote the radical of its module category. The authors showed with Sinha that the stable rank of a special biserial algebra $\Lambda$,…

The following pcf results are proved: 1. Assume that kappa > aleph_0 is a weakly compact cardinal. Let mu > 2^kappa be a singular cardinal of cofinality kappa. Then for every regular lambda < pp^+_{Gamma(kappa)} (mu) there is an increasing…

We classify 1-tilting classes over an arbitrary commutative ring. As a consequence, we classify all resolving subcategories of finitely presented modules of projective dimension at most 1. Both these collections are in 1-1 correspondence…

We use algorithmic methods from online learning to explore some important objects at the intersection of model theory and combinatorics, and find natural ways that algorithmic methods can detect and explain (and improve our understanding…