Given a model M and a temporal logic formula φ[?], where ? is a placeholder, the query checking problem, as defined for the case of CTL by Chan in 2000, is to find the strongest propositional formula f such that M |= φ[? ← f ]. The motivation for solving this problem is, among other things, to get insight on the model. We consider various objectives to the LTL query-checking problem, and study ...

We consider VC-minimal theories admitting unpackable generating families, and show that in such theories, forking of formulae over a model M is equivalent to containment in global types definable over M , generalizing a result of Dolich on o-minimal theories in [4].

Let T be an almost strongly minimal theory. Work inside a monster model M of T . Let M be a model (a small elementary substructure of M). If G is an M -definable group, and H is an M -definable subgroup, we can consider the homogeneous space G/H with the left-action by G. We will define “etale cohomology groups” H M(G/H,A) for all n ≥ 0 and all abelian groups A. We would like the following thin...

In abstract elementary classes limit models are sometimes the appropriate substitute for saturated models. For Galois-stable abstract elementary classes which satisfy the amalgamation property, we prove under the assumption that there is a mildly behaved dependence relation, that for any model M , any two limit models over M of the same cardinality are isomorphic. This is useful in dealing with...

Given a Heath–Jarrow–Morton (HJM) interest rate model M and a parametrized family of finite dimensional forward rate curves G, this paper provides a technique for projecting the infinite dimensional forward rate curve rt given by M onto the finite dimensional manifold G. The Stratonovich dynamics of the projected finite dimensional forward curve are derived and it is shown that, under the regul...

As an application of the method used to obtain the result above, we will obtain the consistency of b = ω1 < s = κ where b is the bounding number, s is the splitting number and κ is an arbitrary regular cardinal. Suppose ν ≥ δ. Begin with a model of GCH and adjoin δ-many Cohen reals 〈rα : α ∈ δ〉 followed by ν-many Random reals 〈sξ : ξ ∈ ν〉. That is, if Vδ is the model obtained after the first δ ...

This is an expository note on the Lascar group. We also study the Lascar group over hyperimaginaries, and make some new observations on the strong types over those. In particular we show that in a simple theory, Ltp ≡ stp in real context implies that for hyperimaginary context. The Lascar group introduced by Lascar [8], and related subjects have been studied by many authors ([9][1][7][6][3] and...

Suppose κ is λ-supercompact witnessed by an elementary embedding j : V →M with critical point κ, and further suppose that F is a function from the class of regular cardinals to the class of cardinals satisfying the requirements of Easton’s theorem: (1) ∀α α < cf(F (α)) and (2) α < β =⇒ F (α) ≤ F (β). In this article we address the question: assuming GCH, what additional assumptions are necessar...

In this paper we examine the cardinal structure of inner models that satisfy GCH but do not contain 0. We show, assuming that 0 exists, that such models necessarily contain Mahlo cardinals of high order, but without further assumptions need not contain a cardinal κ which is κ-Mahlo. The principal tools are the Covering Theorem for L and the technique of reverse Easton iteration. Let I denote th...