Related papers: New reals: Can live with them, can live without th…
Noether's first theorem does not establish a one-way explanatory arrow from symmetries to conservation laws, but such an arrow is widely assumed in discussions of the theorem in the physics and philosophy literature. It is argued here that…
For $\lambda$ inaccessible, we may consider $(< \lambda)$-support iteration of some specific $(<\lambda)$-complete $\lambda^+$-c.c. forcing notion. But this fails a "preservation by restricting to a sub-sequence of the forcing, we "correct"…
Theorems crucial in elementary real function theory have proofs in which compactness arguments are used. Despite the introduction in relatively recent literature of each new highly elegant compactness argument, or of an equivalent, this…
In this paper I introduce a new and intuitive first-order foundational theory (where the concept of set is not primitive) and use it to show that the power set of an infinite set does not exist. In particular, proofs of uncountability of a…
We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation is given by inclusion, and existing meets and joins of…
We study uncountable structures similar to the Fra\"iss\'e limits. The standard inductive arguments from the Fra\"iss\'e theory are replaced by forcing, so the structures we obtain are highly sensitive to the universe of set theory. In…
It is often claimed that analysis with infinitesimals requires more substantial use of the Axiom of Choice than traditional elementary analysis. The claim is based on the observation that the hyperreals entail the existence of nonprincipal…
In this paper, we prove several theorems on systems of polynomials with at least one positive real zero based on the theory of conceive polynomials. These theorems provide sufficient conditions for systems of multivariate polynomials…
Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize…
We review the theory of renewal reward processes, which describes renewal processes that have some cost or reward associated with each cycle. We present a new simplified proof of the renewal reward theorem that mimics the proof of the…
Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…
Exact real computation is an alternative to floating-point arithmetic where operations on real numbers are performed exactly, without the introduction of rounding errors. When proving the correctness of an implementation, one can focus…
The notion of a real-valued function is central to mathematics, computer science, and many other scientific fields. Despite this importance, there are hardly any positive results on decision procedures for predicate logical theories that…
Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In…
Theoretical analysis proves that human survivability is dominated by an unusual physical, rather than biological, mechanism, which yields an exact law. The law agrees with all experimental data, but, contrary to existing theories, it is the…
We present an illative system I_s of classical higher-order logic with subtyping and basic inductive types. The system I_s allows for direct definitions of partial and general recursive functions, and provides means for handling functions…
It is proved that the first-order theory of the structure (N,mod) is undecidable. Here mod denotes the operation of computing the remainder for any division between positive integers; i.e. x mod y is the remainder obtained by the division x…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
A first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…