We develop various aspects of the nite model theory of L k (9) and L k 1! (9). We establish the optimality of normal forms for L k 1! (9) over the class of nite structures and demonstrate separations among descriptive complexity classes within L k 1! (9). We establish negative results concerning preservation theorems for L k (9) and L k 1! (9). We introduce a generalized notion of preservation ...

A. Csaszar introduced and extensively studied the notion of generalized open sets. Following Csazar, we introduce a new notion superconnected. The main purpose of this paper is to study generalized superconnected spaces. Various characterizations of generalized superconnected spaces and preservation theorems are discussed.

A major theme of [12] is preservation theorems for iterated forcing. These are theorems of the form “if 〈Pξ : ξ ≤ κ〉 is a countable support forcing iteration based on 〈Q̇ξ : ξ < κ〉 and each Q̇ξ has property such-and-such then Pκ has property thus-and-so.” The archetypal preservation theorem is the Fundamental Theorem of Proper Forcing [12, chapter III], which states that if each Q̇ξ is proper in V...

I prove forcing preservation theorems for products of definable partial orders preserving cofinality of the meager or null ideal. Rectangular Ramsey theorems for the related ideals follow from the proofs.

I will prove iteration and product preservation theorems related to Ppoint preservation based on the first part of the paper. I will also provide counterexamples to possible strengthenings of the presented results.

a. csaszar introduced and extensively studied the notionof generalized open sets. following csazar, we introduce a new notionsuperconnected. the main purpose of this paper is to study generalizedsuperconnected spaces. various characterizations of generalized super-connected spaces and preservation theorems are discussed.

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 th...

We develop various aspects of the finite model theory of Lk(there exists) and Lk∞omega(there exists). We establish the optimality of normal forms for Lk∞omega(there exists) over the class of finite structures and demonstrate separations over the class of finite structures and demonstrate separations among descriptive complexity classes within Lk∞omega(there exists). We establish negative result...

This technical report presents the full proofs for the type preservation and effect soundness theorems of the type system presented in the article “Lightweight Polymorphic Effects”.