We prove a variety of theorems about stationary set reflection and concepts related to internal approachability. that an implication Fuchino-Usuba relating version Strong Chang's Conjecture cannot be reversed; strengthen simplify some results Krueger forcing axioms approachability; other are sharp. also adapt ideas Woodin unify many arguments in the literature involving preservation axioms.

We present preservation theorems for countable support iteration of nep forcing notions satisfying “old reals are not Lebesgue null” (section 6) and “old reals are not meager” (section 5). (Nep is a generalization of Suslin proper.) We also give some results for general Suslin ccc ideals (the results are summarized in a diagram on page 17). This paper is closely related to [She98, XVIII, §3] an...

We propose a new, logical, approach to the decidability problem for the Straubing and Brzozowski hierarchies based on the preservation theorems from model theory, on a theorem of Higman, and on the Rabin tree theorem. In this way, we get purely logical, short proofs for some known facts on decidability, which might be of methodological interest. Our approach is also applicable to some other sim...

Various theorems for the preservation of set-theoretic axioms under forcing are proved, regarding both forcing axioms and axioms true in the Levy-Collapse. These show in particular that certain applications of forcing axioms require to add generic countable sequences high up in the set-theoretic hierarchy even before collapsing everything down to א1. Later we give applications, among them the c...

We look at various preservation theorems of classical logic ((rst of all, Los-Tarski theorem) which fail in the context of nite models , and examine the extent of their failure. In some cases, even if the old correspondence between syntactical and semantical properties does not hold, one can nd a new semantical counterpart for the syntacti-cal property, and vice versa-a new syntactical counterp...

In this paper the concept of intuitionistic fuzzy slightly precontinuous functions are introduced and studied. Intuitionistic fuzzy slightly precontinuity generalize intuitionistic fuzzy precontinuity. Besides giving characterizations and basic properties of this function, preservation theorems of intuitionistic fuzzy slightly precontinuous are also obtained. We also study relationships between...

Keywords: Systems with time delays Distributed delay Exponential stability Perturbations a b s t r a c t We consider preservation of exponential stability for a system of linear equations with a distributed delay under the addition of new terms and a delay perturbation. As particular cases, the system includes models with concentrated delays and systems of integrodifferential equations. Our met...

In this paper we consider billiards in a square with a barrier. We use Ratner’s theorem to compute the asymptotics for the number of closed orbits.

We (i.e. I) present a simplified version of Shelah’s “preserving a little implies preserving much”: If I is the ideal generated by a Suslin ccc forcing (e.g. Lebesque– null or meager), and P is a Suslin forcing, and P is I–preserving (i.e. it doesn’t make any positive Borel–set small), then P preserves generics over candidates and therefore is strongly I–preserving (i.e. doesn’t make any positi...

We (i.e. I) present a simplified version of Shelah’s “preserving a little implies preserving much”: If I is the ideal generated by a Suslin ccc forcing (e.g. Lesbeque– null or meager), and P is a Suslin forcing, and P is I–preserving (i.e. it doesn’t make any positive Borel–set small), then P preserves generics over candidates and therefore is strongly I–preserving (i.e. doesn’t make any positi...