Related papers: A Boolean Algebraic Approach to Semiproper Iterati…
We present a method to simplify expressions in the context of an equational theory. The basic ideas and concepts of the method have been presented previously elsewhere but here we tackle the difficult task of making it efficient in…
While statement autoformalization has advanced rapidly, full-theorem autoformalization remains largely unexplored. Existing iterative refinement methods in statement autoformalization typically improve isolated aspects of formalization,…
This is an expository paper about several sophisticated forcing techniques closely related to standard finite support iterations of ccc partial orders. We focus on the four topics of ultrapowers of forcing notions, iterations along…
A Rough semiring $(T,\Delta,\nabla)$ is considered to describe a special distributive Rough semiring known as a Rough bi-Heyting algebra. A bi-Heyting algebra is an extension of boolean algebra and it is accomplished by weaker notion of…
Recursive queries have been traditionally studied in the framework of datalog, a language that restricts recursion to monotone queries over sets, which is guaranteed to converge in polynomial time in the size of the input. But modern big…
In a self-contained way, we deal with revised countable support iterated forcing for the reals. We improve theorems on preservation of the property UP, weaker than semi proper, and we hopefully improve the presentation. We continue [Sh:b,…
We present a labelled sequent calculus for Boolean BI, a classical variant of O'Hearn and Pym's logic of Bunched Implication. The calculus is simple, sound, complete, and enjoys cut-elimination. We show that all the structural rules in our…
We study sheaves in the context of a duality theory for lattice structure endowed with extra operations, and in the context of forcing in a topos. Using Sheaf duality theory of Comer for cylindric algebras, we give a representation theorem…
We introduce several properties of forcing notions which imply that their lambda-support iterations are lambda-proper. Our methods and techniques refine those studied in math.LO/9906024, math.LO/0210205, math.LO/0508272 and math.LO/0605067,…
It was realized early on that topologies can model constructive systems, as the open sets form a Heyting algebra. After the development of forcing, in the form of Boolean-valued models, it became clear that, just as over ZF any…
Let I be a sigma-ideal sigma-generated by a projective collection of closed sets. The forcing with I-positive Borel sets is proper and adds a single real r of an almost minimal degree: if s is a real in V[r] then s is Cohen generic over V…
We introduce a refined immersed boundary (IB) methodology that is better-than-first-order accurate in practice, while preserving key properties of "continuous-forcing" IB approaches that retain a singular source term in the governing…
We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to 'recover' the properties of classical…
Shelah introduced the revised countable support (RCS) iteration to iterate semiproperness. This was an endpoint in the search for an iteration of a weak condition, still implying that aleph1 is preserved. Dieter Donder found a better…
The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…
We show that while the length $\omega$ iterated ultrapower by a normal ultrafilter is a Boolean ultrapower by the Boolean algebra of Prikry forcing, it is consistent that no iteration of length greater than $\omega$ (of the same ultrafilter…
Semi-structured explanation depicts the implicit process of a reasoner with an explicit representation. This explanation highlights how available information in a specific query is utilised and supplemented with information a reasoner…
Shelah shows that certain revised countable support (RCS) iterations do not add reals. His motivation is to establish the independence (relative to large cardinals) of Avraham's problem on the existence of uncountable non-constuctible…
Beyond the great cognitive powers showcased by language models, it is crucial to scrutinize whether their reasoning capabilities stem from strong generalization or merely exposure to relevant data. As opposed to constructing increasingly…
We consider the problem of searching for proofs in sequential presentations of logics with multiplicative (or intensional) connectives. Specifically, we start with the multiplicative fragment of linear logic and extend, on the one hand, to…